8. Time Series.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "#### Time Series is am important form of structured data in different fields. eg - finance, economics, physics, etc.\n",
    "#### Anything observed or measured at many points in time forms a time series.\n",
    "#### Many Time Series are 'fixed frequency' i.e. data points occur at regular intervals.\n",
    "#### It can also be 'irregular' i.e without a fixed unit of time or offset between units.\n",
    "#### There are different ways to mark and refer time series, some of which are:\n",
    "####     1. Timestamps - specific instants of time\n",
    "####     2. Fixed periods - months (eg - Jan 2017) or full year (eg - 2010)\n",
    "####     3. Intervals of Time - defined by start and end timestamp. Fixed Periods can be thought of as special cases of Intervals.\n",
    "####     4. Experiment or elapsed time - Each timestamp is a measure of time relative to a particular start time.\n",
    "#### pandas has many nuilt-in tools and algorithms for time series. They help to easily dice, aggregate and resample time-series.\n",
    "#### TIP - pandas also supports indexes based on 'time deltas', which are useful for representing experiment or elapsed time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Date and Time Data Types and Tools\n",
    "#### The Python standard library has data types for date and time data and calendar-related functionality. The modules 'datetime', 'time' and 'calendar' are main modules.\n",
    "#### 'datetime' stores both date and time down to microsecond. 'timedelta' represents temporal difference between 2 datetime objects.\n",
    "#### You can add or subtract 'timedelta' or its multiple to a datetime object to get a shifted object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2018, 8, 24, 14, 54, 13, 736240)"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from datetime import datetime\n",
    "\n",
    "now = datetime.now()\n",
    "now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2018, 8, 24)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "now.year, now.month, now.day"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.timedelta(926, 56700)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = datetime(2011, 1, 7) - datetime(2008, 6, 24, 8, 15)\n",
    "delta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "926"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta.days"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56700"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta.seconds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2011, 1, 19, 0, 0)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from datetime import timedelta\n",
    "\n",
    "start = datetime(2011, 1, 7)\n",
    "start + timedelta(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2010, 12, 14, 0, 0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "start - 2 * timedelta(12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Converting Between String and Datetime\n",
    "#### You can format datetime objects and pandas' Timestamp objects as strings using 'str' or 'strftime' passing the format specification.\n",
    "#### You can use the same format codes to convert strings to dates using 'datetime.strptime'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2011-01-03 00:00:00'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp = datetime(2011, 1, 3)\n",
    "\n",
    "str(stamp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2011-01-03'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp.strftime('%Y-%m-%d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2011, 1, 3, 0, 0)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "value = '2011-01-03'\n",
    "\n",
    "datetime.strptime(value, '%Y-%m-%d')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[datetime.datetime(2011, 7, 6, 0, 0), datetime.datetime(2011, 8, 6, 0, 0)]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datestrs = ['7/6/2011', '8/6/2011']\n",
    "\n",
    "[datetime.strptime(x, '%m/%d/%Y') for x in datestrs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 'datetime.strptime' is a good way to parse date with known format. But it can be a bit annoying to write a format each time.\n",
    "#### In this case, you can use 'parser.parse' from third-party 'dateutil' package. It is capable of parsing most human-intelligible date representations.\n",
    "#### Eg - day appearing before month in dates outside USA is common, for which we can use 'dayfirst=True'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2011, 1, 3, 0, 0)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from dateutil.parser import parse\n",
    "\n",
    "parse('2011-01-03')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(1997, 1, 13, 22, 45)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parse('Jan 13, 1997 10:45 PM')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2011, 12, 6, 0, 0)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parse('6/12/2011', dayfirst=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### pandas is oriented towards working with arrays of dates either as index or a column in a DataFrame.\n",
    "#### The 'to_datetime' method parses different kinds of date representations. Standard formats (eg - ISO 8601) can be parsed quickly.\n",
    "#### It is also able to handle values that should be considered missing. (eg - none, empty string, etc.)\n",
    "#### datetime objects have number of locale-specific formatting options for systems in other countries or languages. eg - abbreviated month names are different in German and French systems.\n",
    "#### NOTE - NaT (Not a Time) is pandas' null value for timestamp data.\n",
    "#### CAUTION - dateutil.parser is useful but imperfect tool. It may even recognize some strings as dates. eg - '42' as year 2042."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2011-07-06 12:00:00', '2011-08-06 00:00:00'], dtype='datetime64[ns]', freq=None)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "datestrs = ['2011-07-06 12:00:00', '2011-08-06 00:00:00']\n",
    "pd.to_datetime(datestrs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2011-07-06 12:00:00', '2011-08-06 00:00:00', 'NaT'], dtype='datetime64[ns]', freq=None)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx = pd.to_datetime(datestrs + [None])\n",
    "idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NaT"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False, False,  True])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.isnull(idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Series Basics\n",
    "#### The most basic time series object in pandas is a Series indexed by timestamps. It is represented external to pandas as Python strings or datetime objects.\n",
    "#### Under the hood, datetime objects are put in DatetimeIndex.\n",
    "#### Like other Series, arithematic operations between differently indexed time series automatically align on the dates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011-01-02   -0.620602\n",
       "2011-01-05    0.654620\n",
       "2011-01-07    0.669635\n",
       "2011-01-08   -0.541739\n",
       "2011-01-10   -0.434964\n",
       "2011-01-12    0.054170\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "dates = [datetime(2011, 1, 2), datetime(2011, 1, 5),\n",
    "        datetime(2011, 1, 7), datetime(2011, 1, 8),\n",
    "        datetime(2011, 1, 10), datetime(2011, 1, 12)]\n",
    "\n",
    "ts = pd.Series(np.random.randn(6), index=dates)\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2011-01-02', '2011-01-05', '2011-01-07', '2011-01-08',\n",
       "               '2011-01-10', '2011-01-12'],\n",
       "              dtype='datetime64[ns]', freq=None)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011-01-02   -1.241204\n",
       "2011-01-05         NaN\n",
       "2011-01-07    1.339270\n",
       "2011-01-08         NaN\n",
       "2011-01-10   -0.869929\n",
       "2011-01-12         NaN\n",
       "dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts + ts[::2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### pandas stores timestamps using NumPy's 'datetime64' data type at nanosecond resolution.\n",
    "#### Scalar values from 'DatetimeIndex' are pandas 'Timestamp' objects. A 'Timestamp' can be substituted anywhere you would use a 'datetime' object.\n",
    "#### It can store frequency information and understands time zone conversions and other manipulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('<M8[ns]')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.index.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-01-02 00:00:00')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp = ts.index[0]\n",
    "stamp"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Indexing, Selection, Subsetting\n",
    "#### Time Series behaves like any other pandas.Series when indexing and selecting based on label.\n",
    "#### Conveniently, you can pass a string that is interpretable as a date as index.\n",
    "#### For longer time series, to get easy slices od data, you can pass only a year or year and month.\n",
    "#### You can also slice using 'datetime' objects.\n",
    "#### Because most time series data are ordered chronologically, you can slice with timestanps not present in the series to perform range query. You can also pass string, datetime or timestamp for this indexing.\n",
    "#### Slicing in this manner produces views on the source like slicing NumPy arrays. No data is copied and modificatiosn will be reflected in original data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6696347769484791"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp = ts.index[2]\n",
    "ts[stamp]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.43496431723264006"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts['1/10/2011']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.43496431723264006"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts['20110110']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01   -1.327905\n",
       "2000-01-02    0.389855\n",
       "2000-01-03    0.038276\n",
       "2000-01-04   -1.225384\n",
       "2000-01-05    0.704407\n",
       "2000-01-06    0.200485\n",
       "2000-01-07    0.280085\n",
       "2000-01-08    0.314965\n",
       "2000-01-09   -0.241732\n",
       "2000-01-10    0.631419\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longer_ts = pd.Series(np.random.randn(1000),\n",
    "                     index=pd.date_range('1/1/2000', periods=1000))\n",
    "longer_ts[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2001-01-01    1.581130\n",
       "2001-01-02    0.167098\n",
       "2001-01-03   -0.816911\n",
       "2001-01-04    0.302942\n",
       "2001-01-05    0.968706\n",
       "2001-01-06    0.779146\n",
       "2001-01-07   -1.523483\n",
       "2001-01-08   -0.724681\n",
       "2001-01-09   -0.178921\n",
       "2001-01-10    0.557737\n",
       "2001-01-11   -0.173565\n",
       "2001-01-12    0.651159\n",
       "2001-01-13   -2.503144\n",
       "2001-01-14    0.178297\n",
       "2001-01-15    0.488626\n",
       "2001-01-16    0.653233\n",
       "2001-01-17    0.334088\n",
       "2001-01-18    0.249476\n",
       "2001-01-19    0.476417\n",
       "2001-01-20   -0.720533\n",
       "2001-01-21   -0.960502\n",
       "2001-01-22   -0.403528\n",
       "2001-01-23   -0.424601\n",
       "2001-01-24   -0.015189\n",
       "2001-01-25   -1.586064\n",
       "2001-01-26    0.206113\n",
       "2001-01-27   -2.213696\n",
       "2001-01-28    0.246418\n",
       "2001-01-29    1.175788\n",
       "2001-01-30   -0.839724\n",
       "                ...   \n",
       "2001-12-02   -0.908207\n",
       "2001-12-03   -0.113172\n",
       "2001-12-04   -0.583514\n",
       "2001-12-05    1.007903\n",
       "2001-12-06    1.234086\n",
       "2001-12-07   -0.882931\n",
       "2001-12-08   -1.046718\n",
       "2001-12-09   -0.726555\n",
       "2001-12-10   -1.761837\n",
       "2001-12-11    0.819854\n",
       "2001-12-12    0.279015\n",
       "2001-12-13   -0.457892\n",
       "2001-12-14   -0.695965\n",
       "2001-12-15    1.223902\n",
       "2001-12-16    0.771305\n",
       "2001-12-17   -0.037302\n",
       "2001-12-18    0.143658\n",
       "2001-12-19   -0.507868\n",
       "2001-12-20   -0.261718\n",
       "2001-12-21    0.590917\n",
       "2001-12-22    0.067249\n",
       "2001-12-23   -1.703787\n",
       "2001-12-24    1.021178\n",
       "2001-12-25   -2.458587\n",
       "2001-12-26    1.317673\n",
       "2001-12-27    0.819459\n",
       "2001-12-28   -0.302990\n",
       "2001-12-29   -0.501248\n",
       "2001-12-30   -1.017126\n",
       "2001-12-31   -1.384842\n",
       "Freq: D, Length: 365, dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longer_ts['2001']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2001-05-01   -0.578289\n",
       "2001-05-02    0.514882\n",
       "2001-05-03   -2.813481\n",
       "2001-05-04   -0.013797\n",
       "2001-05-05   -0.930187\n",
       "2001-05-06   -0.026023\n",
       "2001-05-07    0.684279\n",
       "2001-05-08    0.927434\n",
       "2001-05-09    1.185822\n",
       "2001-05-10    0.739293\n",
       "2001-05-11   -2.481568\n",
       "2001-05-12    0.385364\n",
       "2001-05-13    0.812606\n",
       "2001-05-14   -0.636680\n",
       "2001-05-15    0.462309\n",
       "2001-05-16    0.480784\n",
       "2001-05-17   -1.428652\n",
       "2001-05-18   -0.454706\n",
       "2001-05-19    1.627808\n",
       "2001-05-20   -0.334482\n",
       "2001-05-21   -0.603552\n",
       "2001-05-22    1.918634\n",
       "2001-05-23   -1.425140\n",
       "2001-05-24   -0.195504\n",
       "2001-05-25    0.525058\n",
       "2001-05-26    1.181563\n",
       "2001-05-27   -0.891890\n",
       "2001-05-28   -2.671364\n",
       "2001-05-29    0.875528\n",
       "2001-05-30   -0.788606\n",
       "2001-05-31    0.893880\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longer_ts['2001-05']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6696347769484791"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts[datetime(2011, 1, 7)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011-01-02   -0.620602\n",
       "2011-01-05    0.654620\n",
       "2011-01-07    0.669635\n",
       "2011-01-08   -0.541739\n",
       "2011-01-10   -0.434964\n",
       "2011-01-12    0.054170\n",
       "dtype: float64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011-01-07    0.669635\n",
       "2011-01-08   -0.541739\n",
       "2011-01-10   -0.434964\n",
       "dtype: float64"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts['1/6/2011':'1/11/2011']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### There is an equivalent method for instance as well called 'truncate', which slices Series between two dates.\n",
    "#### All of the above holds true for DataFrame as well, based on indexing on its rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011-01-02   -0.620602\n",
       "2011-01-05    0.654620\n",
       "2011-01-07    0.669635\n",
       "2011-01-08   -0.541739\n",
       "dtype: float64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.truncate(after='1/9/2011')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2001-05-02</th>\n",
       "      <td>-0.695881</td>\n",
       "      <td>-1.663806</td>\n",
       "      <td>1.190218</td>\n",
       "      <td>-0.473666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-05-09</th>\n",
       "      <td>0.021602</td>\n",
       "      <td>-0.114717</td>\n",
       "      <td>-0.994597</td>\n",
       "      <td>-0.672968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-05-16</th>\n",
       "      <td>1.398907</td>\n",
       "      <td>-0.205220</td>\n",
       "      <td>-0.124262</td>\n",
       "      <td>2.283874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-05-23</th>\n",
       "      <td>0.431852</td>\n",
       "      <td>-0.253309</td>\n",
       "      <td>-0.319060</td>\n",
       "      <td>0.723475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-05-30</th>\n",
       "      <td>-0.847489</td>\n",
       "      <td>0.285182</td>\n",
       "      <td>0.186877</td>\n",
       "      <td>1.487554</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Colorado     Texas  New York      Ohio\n",
       "2001-05-02 -0.695881 -1.663806  1.190218 -0.473666\n",
       "2001-05-09  0.021602 -0.114717 -0.994597 -0.672968\n",
       "2001-05-16  1.398907 -0.205220 -0.124262  2.283874\n",
       "2001-05-23  0.431852 -0.253309 -0.319060  0.723475\n",
       "2001-05-30 -0.847489  0.285182  0.186877  1.487554"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dates = pd.date_range('1/1/2000', periods=100, freq='W-WED')\n",
    "\n",
    "long_df = pd.DataFrame(np.random.randn(100, 4),\n",
    "                      index=dates,\n",
    "                      columns = ['Colorado', 'Texas',\n",
    "                                'New York', 'Ohio'])\n",
    "\n",
    "long_df.loc['5-2001']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time Series with Duplicate Indices\n",
    "#### In some scenarios, you may have multiple data observations falling on particular timestamp. You can determine if the index is not unique by using 'is_unique' property.\n",
    "#### Indexing in such a time series will either produce scalar values or slices, depending on condition that timestamp is duplicated or not.\n",
    "#### A way to aggregate on non-unique timestamps is to use 'groupby' and pass 'level=0'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01    0\n",
       "2000-01-02    1\n",
       "2000-01-02    2\n",
       "2000-01-02    3\n",
       "2000-01-03    4\n",
       "dtype: int32"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dates = pd.DatetimeIndex(['1/1/2000', '1/2/2000', '1/2/2000',\n",
    "                         '1/2/2000', '1/3/2000'])\n",
    "dup_ts = pd.Series(np.arange(5), index=dates)\n",
    "dup_ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dup_ts.index.is_unique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dup_ts['1/3/2000']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-02    1\n",
       "2000-01-02    2\n",
       "2000-01-02    3\n",
       "dtype: int32"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dup_ts['1/2/2000']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01    0\n",
       "2000-01-02    2\n",
       "2000-01-03    4\n",
       "dtype: int32"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped = dup_ts.groupby(level=0)\n",
    "\n",
    "grouped.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01    1\n",
       "2000-01-02    3\n",
       "2000-01-03    1\n",
       "dtype: int64"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped.count()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Date Ranges, Frequencies, and Shifting\n",
    "#### Generic time series in pandas are assumed to be irregular i.e. no fixed frequency.\n",
    "#### Sometimes, it is necessary to work with relatively fixed frequency, even if it means introducing missing values in the series.\n",
    "#### pndas has full suite of standard time series frequencies and tools for resampling, interferring frequencies, and generating fixed-frequency date ranges. eg - You can convert sample time series into fixd daily frequency using 'resample'. Using string 'D' for 'daily frequency'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011-01-02   -0.620602\n",
       "2011-01-05    0.654620\n",
       "2011-01-07    0.669635\n",
       "2011-01-08   -0.541739\n",
       "2011-01-10   -0.434964\n",
       "2011-01-12    0.054170\n",
       "dtype: float64"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "resampler = ts.resample('D')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndexResampler [freq=<Day>, axis=0, closed=left, label=left, convention=start, base=0]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resampler"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating Date Ranges\n",
    "#### 'pandas.date_range' is responsible for generating 'DatetimeIndex' with indicated length based on particulare frequency.\n",
    "#### By default, it generates daily timestamps. If you only pass either start or end date, you must also pass number of periods as well. \n",
    "#### The start and end dates define strict boundaries for generated date index.\n",
    "#### Eg - to get last business day each month, you would pass 'BM' frequency.\n",
    "#### By default, date_range preserves the time of the start or end timestamp.\n",
    "#### You can even create set of timestamps normalized to midnight using the 'normalize' option."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-04-01', '2012-04-02', '2012-04-03', '2012-04-04',\n",
       "               '2012-04-05', '2012-04-06', '2012-04-07', '2012-04-08',\n",
       "               '2012-04-09', '2012-04-10', '2012-04-11', '2012-04-12',\n",
       "               '2012-04-13', '2012-04-14', '2012-04-15', '2012-04-16',\n",
       "               '2012-04-17', '2012-04-18', '2012-04-19', '2012-04-20',\n",
       "               '2012-04-21', '2012-04-22', '2012-04-23', '2012-04-24',\n",
       "               '2012-04-25', '2012-04-26', '2012-04-27', '2012-04-28',\n",
       "               '2012-04-29', '2012-04-30', '2012-05-01', '2012-05-02',\n",
       "               '2012-05-03', '2012-05-04', '2012-05-05', '2012-05-06',\n",
       "               '2012-05-07', '2012-05-08', '2012-05-09', '2012-05-10',\n",
       "               '2012-05-11', '2012-05-12', '2012-05-13', '2012-05-14',\n",
       "               '2012-05-15', '2012-05-16', '2012-05-17', '2012-05-18',\n",
       "               '2012-05-19', '2012-05-20', '2012-05-21', '2012-05-22',\n",
       "               '2012-05-23', '2012-05-24', '2012-05-25', '2012-05-26',\n",
       "               '2012-05-27', '2012-05-28', '2012-05-29', '2012-05-30',\n",
       "               '2012-05-31', '2012-06-01'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = pd.date_range('2012-04-01', '2012-06-01')\n",
    "index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-04-01', '2012-04-02', '2012-04-03', '2012-04-04',\n",
       "               '2012-04-05', '2012-04-06', '2012-04-07', '2012-04-08',\n",
       "               '2012-04-09', '2012-04-10', '2012-04-11', '2012-04-12',\n",
       "               '2012-04-13', '2012-04-14', '2012-04-15', '2012-04-16',\n",
       "               '2012-04-17', '2012-04-18', '2012-04-19', '2012-04-20'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.date_range(start='2012-04-01', periods=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-06-01', '2012-06-02', '2012-06-03', '2012-06-04',\n",
       "               '2012-06-05', '2012-06-06', '2012-06-07', '2012-06-08',\n",
       "               '2012-06-09', '2012-06-10', '2012-06-11', '2012-06-12',\n",
       "               '2012-06-13', '2012-06-14', '2012-06-15', '2012-06-16',\n",
       "               '2012-06-17', '2012-06-18', '2012-06-19', '2012-06-20'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.date_range(start='2012-06-01', periods=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2000-01-31', '2000-02-29', '2000-03-31', '2000-04-28',\n",
       "               '2000-05-31', '2000-06-30', '2000-07-31', '2000-08-31',\n",
       "               '2000-09-29', '2000-10-31', '2000-11-30'],\n",
       "              dtype='datetime64[ns]', freq='BM')"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.date_range('2000-01-01', '2000-12-01', freq='BM')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-05-02 12:56:31', '2012-05-03 12:56:31',\n",
       "               '2012-05-04 12:56:31', '2012-05-05 12:56:31',\n",
       "               '2012-05-06 12:56:31'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Timestamp of 12:56:31 preserved\n",
    "pd.date_range('2012-05-02 12:56:31', periods=5) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-05-02', '2012-05-03', '2012-05-04', '2012-05-05',\n",
       "               '2012-05-06'],\n",
       "              dtype='datetime64[ns]', freq='D')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Timestamp normalized to midnight i.e. 12:56:31 removed\n",
    "pd.date_range('2012-05-02 12:56:31', periods=5, normalize=True) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frequencies and Date Offsets\n",
    "#### Frequencies in pandas are composed of 'base frequency' and 'multiplier'. Base frequencies are typicall referred by string alias. eg - 'M' for monthly, 'H' for hourly.\n",
    "#### For each base frequency, there is a defined object called 'date offset'. eg - hourly can be represented with Hour class.\n",
    "#### You can define a multiple of an offset by passing an integer.\n",
    "#### You never need to explicitly need to create any of the objects. Instead just use string alias. eg - '4H', 'H'. Putting an integer before base frequency creates a multiple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Hour>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas.tseries.offsets import Hour, Minute\n",
    "\n",
    "hour = Hour()\n",
    "hour"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<4 * Hours>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "four_hours = Hour(4)\n",
    "four_hours"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2000-01-01 00:00:00', '2000-01-01 04:00:00',\n",
       "               '2000-01-01 08:00:00', '2000-01-01 12:00:00',\n",
       "               '2000-01-01 16:00:00', '2000-01-01 20:00:00',\n",
       "               '2000-01-02 00:00:00', '2000-01-02 04:00:00',\n",
       "               '2000-01-02 08:00:00', '2000-01-02 12:00:00',\n",
       "               '2000-01-02 16:00:00', '2000-01-02 20:00:00',\n",
       "               '2000-01-03 00:00:00', '2000-01-03 04:00:00',\n",
       "               '2000-01-03 08:00:00', '2000-01-03 12:00:00',\n",
       "               '2000-01-03 16:00:00', '2000-01-03 20:00:00'],\n",
       "              dtype='datetime64[ns]', freq='4H')"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.date_range('2000-01-01', '2000-01-03 23:59', freq='4h')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Offsets can be combined together by addition.\n",
    "#### Rather than passing specific code for frequency, you can pass strings (eg- '1h30min') that will be parsed to the same expression.\n",
    "#### Some frequencies describe data points not evenly spaced (eg - 'M', 'BM' i.e. last business day of the month). These depend on number of days, whether month ends on wekend or not, etc. These are called as 'anchored offsets'.\n",
    "#### NOTE - Users can define their own custom frequency classes to make up for any date logic not available in pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<150 * Minutes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hour(2) + Minute(30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2001-01-01 00:00:00', '2001-01-01 01:30:00',\n",
       "               '2001-01-01 03:00:00', '2001-01-01 04:30:00',\n",
       "               '2001-01-01 06:00:00', '2001-01-01 07:30:00',\n",
       "               '2001-01-01 09:00:00', '2001-01-01 10:30:00',\n",
       "               '2001-01-01 12:00:00', '2001-01-01 13:30:00'],\n",
       "              dtype='datetime64[ns]', freq='90T')"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.date_range('2001-01-01', periods=10, freq='1h30min')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shifting (Leading and Lagging) Data\n",
    "#### \"Shifting\" refers to moving data backward and forward through time. Bot Series and DataFrame have 'shift' method for naive shifts, leaving the index unmodified.\n",
    "#### When we shift, missing data is introduced either at start or end of the series.\n",
    "#### Common use of shift is computing percent changes in time series or multiple time series as DataFrame columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31    1.465225\n",
       "2000-02-29   -0.248406\n",
       "2000-03-31   -0.224189\n",
       "2000-04-30   -1.282125\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts = pd.Series(np.random.randn(4),\n",
    "              index=pd.date_range('1/1/2000', periods=4, freq='M'))\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31         NaN\n",
       "2000-02-29         NaN\n",
       "2000-03-31    1.465225\n",
       "2000-04-30   -0.248406\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.shift(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31   -0.224189\n",
       "2000-02-29   -1.282125\n",
       "2000-03-31         NaN\n",
       "2000-04-30         NaN\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.shift(-2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31         NaN\n",
       "2000-02-29   -1.169534\n",
       "2000-03-31   -0.097492\n",
       "2000-04-30    4.718958\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts / ts.shift(1) -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Because naive shifts leave index unmodified, some data is discarded. But if the frequency is known, it can be passed to shift to advance the timestamps instead of just the data.\n",
    "#### Different frequencies can be passed, giving some flexibility on how to lead and lag the data. eg - 'T' for minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-02-03    1.465225\n",
       "2000-03-03   -0.248406\n",
       "2000-04-03   -0.224189\n",
       "2000-05-03   -1.282125\n",
       "dtype: float64"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.shift(3, freq='D')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31 01:30:00    1.465225\n",
       "2000-02-29 01:30:00   -0.248406\n",
       "2000-03-31 01:30:00   -0.224189\n",
       "2000-04-30 01:30:00   -1.282125\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.shift(1, freq='90T')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Shifting Dates with Offsets\n",
    "#### The pandas date offsets can also be used with 'datetime' or 'Timestamp' objects.\n",
    "#### If you add anchored offset (eg - 'MonthEnd'), the first increment will 'roll forward' a date to the next date based on the frequency rule."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-11-20 00:00:00')"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas.tseries.offsets import Day, MonthEnd\n",
    "\n",
    "now = datetime(2011, 11, 17)\n",
    "now + 3 * Day()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-11-30 00:00:00')"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "now + MonthEnd()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-12-31 00:00:00')"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "now + MonthEnd(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Anchored offsets can explicitly 'roll' dates forward or backward using 'rollforward' and 'rollback' methods.\n",
    "#### One creative use of offsets is to use them with 'groupby'. It groups based on the offset like month end and calculates aggregate value. But the effects can be much easily be implemented using 'resample'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-11-30 00:00:00')"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "offset = MonthEnd()\n",
    "\n",
    "offset.rollforward(now)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-10-31 00:00:00')"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "offset.rollback(now)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-15   -1.051516\n",
       "2000-01-19   -0.384949\n",
       "2000-01-23   -0.710871\n",
       "2000-01-27   -1.063647\n",
       "2000-01-31    1.510837\n",
       "2000-02-04    0.891960\n",
       "2000-02-08    0.182105\n",
       "2000-02-12   -0.447514\n",
       "2000-02-16    1.149756\n",
       "2000-02-20    0.037801\n",
       "2000-02-24   -0.000932\n",
       "2000-02-28    0.160582\n",
       "2000-03-03    0.433708\n",
       "2000-03-07   -0.354192\n",
       "2000-03-11   -0.734012\n",
       "2000-03-15   -0.222640\n",
       "2000-03-19   -0.189905\n",
       "2000-03-23    0.856604\n",
       "2000-03-27    0.543988\n",
       "2000-03-31   -0.431523\n",
       "Freq: 4D, dtype: float64"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts = pd.Series(np.random.randn(20),\n",
    "              index=pd.date_range('1/15/2000', periods=20, freq='4d'))\n",
    "\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31   -0.340029\n",
       "2000-02-29    0.281965\n",
       "2000-03-31   -0.012246\n",
       "dtype: float64"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.groupby(offset.rollforward).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31   -0.340029\n",
       "2000-02-29    0.281965\n",
       "2000-03-31   -0.012246\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('M').mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time Zone Handling\n",
    "#### Working with time zones is considered one of the most unpleasant parts of time series manipulation.\n",
    "#### Hence many users choose to work in 'coordinated universal time' or 'UTC' which is the current International Standard.\n",
    "#### In Python, time zone info comes from third-party 'pytz' library. It exposes the 'Olson database', which is a compilation of world time zone information.\n",
    "#### This is more important for historical data because the 'daylight saving time (DST)' transition dates have been changed numerous times.\n",
    "#### pandas wraps pytz's functionality so you can ignore its API outside of time zone names, which can be found interactively in the docs.\n",
    "#### To get time zone object from pytz, use 'pytz.timezone'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['US/Eastern', 'US/Hawaii', 'US/Mountain', 'US/Pacific', 'UTC']"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pytz\n",
    "\n",
    "pytz.common_timezones[-5:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<DstTzInfo 'America/New_York' LMT-1 day, 19:04:00 STD>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tz = pytz.timezone('America/New_York')\n",
    "tz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time Zone Localization and Conversion\n",
    "#### By default, time series in pandas are 'time zone naive' i.e. the 'tz' field is None.\n",
    "#### We can create date ranges with a set time zone. But conversion from naive to localizeed is handled by 'tz_localize'.\n",
    "#### We can even convert time zones of the time series. eg - EST to UTC\n",
    "#### DateTimeIndex also has the same instance methods like 'tz_localize' and 'tz_convert'.\n",
    "#### CAUTION - Localizing naive timestamps also checks for ambiguous or non-existent times around daylight saving time transitions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-03-09 09:30:00   -0.447691\n",
       "2012-03-10 09:30:00    0.568457\n",
       "2012-03-11 09:30:00   -0.789614\n",
       "2012-03-12 09:30:00    1.585550\n",
       "2012-03-13 09:30:00    1.125298\n",
       "2012-03-14 09:30:00    0.915889\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.date_range('3/9/2012 9:30', periods=6, freq='D')\n",
    "ts = pd.Series(np.random.randn(len(rng)), index=rng)\n",
    "\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "None\n"
     ]
    }
   ],
   "source": [
    "print(ts.index.tz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-03-09 09:30:00+00:00', '2012-03-10 09:30:00+00:00',\n",
       "               '2012-03-11 09:30:00+00:00', '2012-03-12 09:30:00+00:00',\n",
       "               '2012-03-13 09:30:00+00:00', '2012-03-14 09:30:00+00:00',\n",
       "               '2012-03-15 09:30:00+00:00', '2012-03-16 09:30:00+00:00',\n",
       "               '2012-03-17 09:30:00+00:00', '2012-03-18 09:30:00+00:00'],\n",
       "              dtype='datetime64[ns, UTC]', freq='D')"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.date_range('3/9/2012 9:30', periods=10, freq='D', tz='UTC')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-03-09 09:30:00+00:00   -0.447691\n",
       "2012-03-10 09:30:00+00:00    0.568457\n",
       "2012-03-11 09:30:00+00:00   -0.789614\n",
       "2012-03-12 09:30:00+00:00    1.585550\n",
       "2012-03-13 09:30:00+00:00    1.125298\n",
       "2012-03-14 09:30:00+00:00    0.915889\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_utc = ts.tz_localize('UTC')\n",
    "ts_utc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-03-09 09:30:00+00:00', '2012-03-10 09:30:00+00:00',\n",
       "               '2012-03-11 09:30:00+00:00', '2012-03-12 09:30:00+00:00',\n",
       "               '2012-03-13 09:30:00+00:00', '2012-03-14 09:30:00+00:00'],\n",
       "              dtype='datetime64[ns, UTC]', freq='D')"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_utc.index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-03-09 04:30:00-05:00   -0.447691\n",
       "2012-03-10 04:30:00-05:00    0.568457\n",
       "2012-03-11 05:30:00-04:00   -0.789614\n",
       "2012-03-12 05:30:00-04:00    1.585550\n",
       "2012-03-13 05:30:00-04:00    1.125298\n",
       "2012-03-14 05:30:00-04:00    0.915889\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_utc.tz_convert('America/New_York')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-03-09 14:30:00+00:00   -0.447691\n",
       "2012-03-10 14:30:00+00:00    0.568457\n",
       "2012-03-11 13:30:00+00:00   -0.789614\n",
       "2012-03-12 13:30:00+00:00    1.585550\n",
       "2012-03-13 13:30:00+00:00    1.125298\n",
       "2012-03-14 13:30:00+00:00    0.915889\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_eastern = ts.tz_localize('America/New_York')\n",
    "ts_eastern.tz_convert('UTC')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-03-09 15:30:00+01:00   -0.447691\n",
       "2012-03-10 15:30:00+01:00    0.568457\n",
       "2012-03-11 14:30:00+01:00   -0.789614\n",
       "2012-03-12 14:30:00+01:00    1.585550\n",
       "2012-03-13 14:30:00+01:00    1.125298\n",
       "2012-03-14 14:30:00+01:00    0.915889\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_eastern.tz_convert('Europe/Berlin')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-03-09 09:30:00+08:00', '2012-03-10 09:30:00+08:00',\n",
       "               '2012-03-11 09:30:00+08:00', '2012-03-12 09:30:00+08:00',\n",
       "               '2012-03-13 09:30:00+08:00', '2012-03-14 09:30:00+08:00'],\n",
       "              dtype='datetime64[ns, Asia/Shanghai]', freq='D')"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.index.tz_localize('Asia/Shanghai')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operations with Time Zone - Aware Timestamp Objects\n",
    "#### Similar to time-series and date ranges, Timestamp objects can also be localized from naive to time zone-aware and converted from one zone to another.\n",
    "#### We can also pass a time zone when creating a Timestamp. They internally store UTC timestamp value as nanoseconds since the Unix ecpoch (January 1, 1970). This UTC value is invariant between time zone conversions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-03-11 23:00:00-0500', tz='America/New_York')"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp = pd.Timestamp('2011-03-12 04:00')\n",
    "stamp_utc = stamp.tz_localize('utc')\n",
    "\n",
    "stamp_utc.tz_convert('America/New_York')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2011-03-12 04:00:00+0300', tz='Europe/Moscow')"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp_moscow = pd.Timestamp('2011-03-12 04:00', tz = 'Europe/Moscow')\n",
    "stamp_moscow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1299902400000000000"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp_utc.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1299902400000000000"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp_utc.tz_convert('America/New_York').value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### When doing time arithematic with pandas's 'DateOffset' objects, it respects daylight saving time transitions where possible.\n",
    "#### We can check this by using Timestamps taken 30 minutes before and 90 minutes after Daylight Savings Time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2012-03-12 01:30:00-0400', tz='US/Eastern')"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pandas.tseries.offsets import Hour\n",
    "\n",
    "stamp = pd.Timestamp('2012-03-12 01:30', tz='US/Eastern')\n",
    "stamp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2012-03-12 02:30:00-0400', tz='US/Eastern')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp+Hour()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2012-11-04 00:30:00-0400', tz='US/Eastern')"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp = pd.Timestamp('2012-11-04 00:30', tz='US/Eastern')\n",
    "stamp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2012-11-04 01:30:00-0500', tz='US/Eastern')"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stamp + 2 * Hour()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Operations Between Different Time Zones\n",
    "#### If we combine 2 time series from different time zones, the result will be UTC.\n",
    "#### Since timestamps are stored as UTC under the hood, the operation is straightforward and requires no conversion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2012-03-07 09:30:00    0.747242\n",
       "2012-03-08 09:30:00    1.119408\n",
       "2012-03-09 09:30:00    1.822876\n",
       "2012-03-12 09:30:00   -0.404489\n",
       "2012-03-13 09:30:00    1.347233\n",
       "2012-03-14 09:30:00   -0.524334\n",
       "2012-03-15 09:30:00   -0.229219\n",
       "2012-03-16 09:30:00    0.167957\n",
       "2012-03-19 09:30:00    1.282066\n",
       "2012-03-20 09:30:00    0.512213\n",
       "Freq: B, dtype: float64"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.date_range('3/7/2012 9:30', periods=10, freq='B')\n",
    "ts = pd.Series(np.random.randn(len(rng)), index=rng)\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DatetimeIndex(['2012-03-07 09:30:00+00:00', '2012-03-08 09:30:00+00:00',\n",
       "               '2012-03-09 09:30:00+00:00', '2012-03-12 09:30:00+00:00',\n",
       "               '2012-03-13 09:30:00+00:00', '2012-03-14 09:30:00+00:00',\n",
       "               '2012-03-15 09:30:00+00:00'],\n",
       "              dtype='datetime64[ns, UTC]', freq='B')"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts1 = ts[:7].tz_localize('Europe/London')\n",
    "ts2 = ts1[2:].tz_convert('Europe/Moscow')\n",
    "result = ts1 + ts2\n",
    "\n",
    "result.index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Periods and Period Arithemetic\n",
    "#### Periods represent timespans. eg - days, months, quarters, years, etc.\n",
    "#### The 'Period' class represents this data type, needing a string or integers and a frequency.\n",
    "#### Adding or subtracting integers from periods has the effect of shifting by their frequency.\n",
    "#### If 2 periods have same frequency, their difference is number of units between them. eg - days, montds, years, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2007', 'A-DEC')"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = pd.Period(2007, freq='A-DEC')\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2012', 'A-DEC')"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p + 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2005', 'A-DEC')"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p - 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Period('2014', freq='A-DEC') - p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Regular ranges of periods can be constructed using the 'period_range' function.\n",
    "#### The 'PeriodIndex' class stores sequence of periods and can serve as an axis index in any pandas data structure.\n",
    "#### We can also use an array of strings with this class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PeriodIndex(['2000-01', '2000-02', '2000-03', '2000-04', '2000-05', '2000-06'], dtype='period[M]', freq='M')"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.period_range('2000-01-01', '2000-06-30', freq='M')\n",
    "rng"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01   -0.328395\n",
       "2000-02   -0.131419\n",
       "2000-03    0.914989\n",
       "2000-04    0.111193\n",
       "2000-05    0.171494\n",
       "2000-06    1.002652\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(np.random.randn(6), index=rng)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PeriodIndex(['2001Q3', '2002Q2', '2003Q1'], dtype='period[Q-DEC]', freq='Q-DEC')"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "values = ['2001Q3', '2002Q2', '2003Q1']\n",
    "index = pd.PeriodIndex(values, freq='Q-DEC')\n",
    "index"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Period Frequency Conversion\n",
    "#### Periods and PeriodIndex objects can be converted to other frequencies with 'asfreq' method. eg - annual to monthly period.\n",
    "#### You can think of a period as a cursor pointing to a span of time, subdivided by its defined sub-periods.\n",
    "#### When converting from high to lower frequency, pandas determines superperiod depending on where the subperiod \"belongs\". eg - for 'A-JUN' frequency, 'Aug-2007' will belong to 2008 period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2007', 'A-DEC')"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = pd.Period('2007', freq='A-DEC')\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2007-01', 'M')"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.asfreq('M', how='start')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2007-12', 'M')"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.asfreq('M', how='end')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2007', 'A-JUN')"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = pd.Period('2007', freq='A-JUN')\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2006-07', 'M')"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.asfreq('M', 'start')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2007-06', 'M')"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.asfreq('M', 'end')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2008', 'A-JUN')"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = pd.Period('Aug-2007', freq='M')\n",
    "\n",
    "p.asfreq('A-JUN')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Whole PeriodIndex objects or time series can also be converted with same semantics.\n",
    "#### We can change the frequency to indicate what we want at the end of the period. eg - changing frequency as 'B' for having last business day of each year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2006    0.702730\n",
       "2007    0.825189\n",
       "2008   -0.391357\n",
       "2009    0.293876\n",
       "Freq: A-DEC, dtype: float64"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.period_range('2006', '2009', freq='A-DEC')\n",
    "ts = pd.Series(np.random.randn(len(rng)), index=rng)\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2006-01    0.702730\n",
       "2007-01    0.825189\n",
       "2008-01   -0.391357\n",
       "2009-01    0.293876\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.asfreq('M', how='start')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2006-12-29    0.702730\n",
       "2007-12-31    0.825189\n",
       "2008-12-31   -0.391357\n",
       "2009-12-31    0.293876\n",
       "Freq: B, dtype: float64"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.asfreq('B', how='end')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quarterly Period Frequencies\n",
    "#### Quarterly data is standard in accounting, finance, etc. Much of this data is reported relative to a fiscal year end, especially last calendar or business day.\n",
    "#### Period '2012Q4' has different meaning depending on fiscal year end.\n",
    "#### pandas supports all 12 possible quarterly frequencies - Q-JAN through Q-DEC.\n",
    "#### eg - For fiscal year ending in January, 2012Q4 runs from November through January."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2012Q4', 'Q-JAN')"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = pd.Period('2012Q4', freq='Q-JAN')\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2011-11-01', 'D')"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.asfreq('D', 'start')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2012-01-31', 'D')"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.asfreq('D', 'end')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### This makes it easy to do period arithematic. eg - getting timestamp at 4 pm on second-to-last business day of the quarter.\n",
    "#### You can generate quarterly ranges using 'period_range'. Performing arithematic is similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Period('2012-01-30 16:00', 'T')"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p4pm = (p.asfreq('B', 'e') - 1).asfreq('T', 's') + 16 * 60\n",
    "p4pm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Timestamp('2012-01-30 16:00:00')"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p4pm.to_timestamp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2011Q3    0\n",
       "2011Q4    1\n",
       "2012Q1    2\n",
       "2012Q2    3\n",
       "2012Q3    4\n",
       "2012Q4    5\n",
       "Freq: Q-JAN, dtype: int32"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.period_range('2011Q3', '2012Q4', freq='Q-JAN')\n",
    "ts = pd.Series(np.arange(len(rng)), index=rng)\n",
    "\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2010-10-28 16:00:00    0\n",
       "2011-01-28 16:00:00    1\n",
       "2011-04-28 16:00:00    2\n",
       "2011-07-28 16:00:00    3\n",
       "2011-10-28 16:00:00    4\n",
       "2012-01-30 16:00:00    5\n",
       "dtype: int32"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_rng = (rng.asfreq('B', 'e') - 1).asfreq('T', 's') + 16 * 60\n",
    "ts.index = new_rng.to_timestamp()\n",
    "\n",
    "ts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Converting Timestamps to Periods (and Back)\n",
    "#### Series and DataFrame objects indexed by timestamps can be converted to periods with 'to_period' method.\n",
    "#### As periods refer to non-overlapping timespans, one timestamp can belong to only one period for a given frequency. \n",
    "#### While frequency in 'PeriodIndex'is inferred from the timestamps by default, you cn specify any frequency you want.\n",
    "#### Having duplicate periods in the result is also not a problem.\n",
    "#### To convert back to timestamps, use 'to_timestamp'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-31   -0.411243\n",
       "2000-02-29    0.043029\n",
       "2000-03-31   -0.024429\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.date_range('2000-01-01', periods=3, freq='M')\n",
    "ts = pd.Series(np.random.randn(3), index=rng)\n",
    "\n",
    "ts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01   -0.411243\n",
       "2000-02    0.043029\n",
       "2000-03   -0.024429\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pts = ts.to_period()\n",
    "\n",
    "pts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-29   -1.306829\n",
       "2000-01-30   -0.202568\n",
       "2000-01-31   -0.041823\n",
       "2000-02-01    1.010672\n",
       "2000-02-02    0.316045\n",
       "2000-02-03   -2.897992\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.date_range('1/29/2000', periods=6, freq='D')\n",
    "ts2 = pd.Series(np.random.randn(6), index=rng)\n",
    "\n",
    "ts2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01   -1.306829\n",
       "2000-01   -0.202568\n",
       "2000-01   -0.041823\n",
       "2000-02    1.010672\n",
       "2000-02    0.316045\n",
       "2000-02   -2.897992\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts2.to_period('M')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-29   -1.306829\n",
       "2000-01-30   -0.202568\n",
       "2000-01-31   -0.041823\n",
       "2000-02-01    1.010672\n",
       "2000-02-02    0.316045\n",
       "2000-02-03   -2.897992\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pts = ts2.to_period()\n",
    "pts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-29   -1.306829\n",
       "2000-01-30   -0.202568\n",
       "2000-01-31   -0.041823\n",
       "2000-02-01    1.010672\n",
       "2000-02-02    0.316045\n",
       "2000-02-03   -2.897992\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pts.to_timestamp(how='end')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Creating a PeriodIndex from Arrays\n",
    "#### Fixed frequency datasets sometimes have timespan information spread across multiple columns. eg - macroeconomic dataset has year and uqarter in different columns.\n",
    "#### By passing these columns as arrays to EpriodIndex with a frequency, we can combine them to form an index for the DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>quarter</th>\n",
       "      <th>realgdp</th>\n",
       "      <th>realcons</th>\n",
       "      <th>realinv</th>\n",
       "      <th>realgovt</th>\n",
       "      <th>realdpi</th>\n",
       "      <th>cpi</th>\n",
       "      <th>m1</th>\n",
       "      <th>tbilrate</th>\n",
       "      <th>unemp</th>\n",
       "      <th>pop</th>\n",
       "      <th>infl</th>\n",
       "      <th>realint</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2710.349</td>\n",
       "      <td>1707.4</td>\n",
       "      <td>286.898</td>\n",
       "      <td>470.045</td>\n",
       "      <td>1886.9</td>\n",
       "      <td>28.98</td>\n",
       "      <td>139.7</td>\n",
       "      <td>2.82</td>\n",
       "      <td>5.8</td>\n",
       "      <td>177.146</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2778.801</td>\n",
       "      <td>1733.7</td>\n",
       "      <td>310.859</td>\n",
       "      <td>481.301</td>\n",
       "      <td>1919.7</td>\n",
       "      <td>29.15</td>\n",
       "      <td>141.7</td>\n",
       "      <td>3.08</td>\n",
       "      <td>5.1</td>\n",
       "      <td>177.830</td>\n",
       "      <td>2.34</td>\n",
       "      <td>0.74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2775.488</td>\n",
       "      <td>1751.8</td>\n",
       "      <td>289.226</td>\n",
       "      <td>491.260</td>\n",
       "      <td>1916.4</td>\n",
       "      <td>29.35</td>\n",
       "      <td>140.5</td>\n",
       "      <td>3.82</td>\n",
       "      <td>5.3</td>\n",
       "      <td>178.657</td>\n",
       "      <td>2.74</td>\n",
       "      <td>1.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1959.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2785.204</td>\n",
       "      <td>1753.7</td>\n",
       "      <td>299.356</td>\n",
       "      <td>484.052</td>\n",
       "      <td>1931.3</td>\n",
       "      <td>29.37</td>\n",
       "      <td>140.0</td>\n",
       "      <td>4.33</td>\n",
       "      <td>5.6</td>\n",
       "      <td>179.386</td>\n",
       "      <td>0.27</td>\n",
       "      <td>4.06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1960.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2847.699</td>\n",
       "      <td>1770.5</td>\n",
       "      <td>331.722</td>\n",
       "      <td>462.199</td>\n",
       "      <td>1955.5</td>\n",
       "      <td>29.54</td>\n",
       "      <td>139.6</td>\n",
       "      <td>3.50</td>\n",
       "      <td>5.2</td>\n",
       "      <td>180.007</td>\n",
       "      <td>2.31</td>\n",
       "      <td>1.19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     year  quarter   realgdp  realcons  realinv  realgovt  realdpi    cpi  \\\n",
       "0  1959.0      1.0  2710.349    1707.4  286.898   470.045   1886.9  28.98   \n",
       "1  1959.0      2.0  2778.801    1733.7  310.859   481.301   1919.7  29.15   \n",
       "2  1959.0      3.0  2775.488    1751.8  289.226   491.260   1916.4  29.35   \n",
       "3  1959.0      4.0  2785.204    1753.7  299.356   484.052   1931.3  29.37   \n",
       "4  1960.0      1.0  2847.699    1770.5  331.722   462.199   1955.5  29.54   \n",
       "\n",
       "      m1  tbilrate  unemp      pop  infl  realint  \n",
       "0  139.7      2.82    5.8  177.146  0.00     0.00  \n",
       "1  141.7      3.08    5.1  177.830  2.34     0.74  \n",
       "2  140.5      3.82    5.3  178.657  2.74     1.09  \n",
       "3  140.0      4.33    5.6  179.386  0.27     4.06  \n",
       "4  139.6      3.50    5.2  180.007  2.31     1.19  "
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('examples/macrodata.csv')\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1959.0\n",
       "1    1959.0\n",
       "2    1959.0\n",
       "3    1959.0\n",
       "4    1960.0\n",
       "Name: year, dtype: float64"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.year[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    2.0\n",
       "2    3.0\n",
       "3    4.0\n",
       "4    1.0\n",
       "Name: quarter, dtype: float64"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.quarter[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PeriodIndex(['1959Q1', '1959Q2', '1959Q3', '1959Q4', '1960Q1', '1960Q2',\n",
       "             '1960Q3', '1960Q4', '1961Q1', '1961Q2',\n",
       "             ...\n",
       "             '2007Q2', '2007Q3', '2007Q4', '2008Q1', '2008Q2', '2008Q3',\n",
       "             '2008Q4', '2009Q1', '2009Q2', '2009Q3'],\n",
       "            dtype='period[Q-DEC]', length=203, freq='Q-DEC')"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "index = pd.PeriodIndex(year=data.year, quarter=data.quarter,\n",
    "                      freq='Q-DEC')\n",
    "index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1959Q1    0.00\n",
       "1959Q2    2.34\n",
       "1959Q3    2.74\n",
       "1959Q4    0.27\n",
       "1960Q1    2.31\n",
       "1960Q2    0.14\n",
       "1960Q3    2.70\n",
       "1960Q4    1.21\n",
       "1961Q1   -0.40\n",
       "1961Q2    1.47\n",
       "Freq: Q-DEC, Name: infl, dtype: float64"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.index=index\n",
    "\n",
    "data.infl[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resampling and Frequency Conversion\n",
    "#### Resampling is the process of converting a time series from one frequency to another.\n",
    "#### Aggregating higher frequency data to lower frequency is called 'downsampling'. Converting lower frequency data to higher frequency is called 'upsampling'.\n",
    "#### There can be other instances of sampling not falling in these categories. eg - W-WED to W-FRI.\n",
    "#### pandas objects are equipped with 'resample' method, which is the wrokhorse function for frequency conversion.\n",
    "#### It has a similar API as 'groupby'. You call 'resample' to group the data and then call an aggregation function.\n",
    "#### 'resample' is a flexible and high-performance function that can process very large time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2001-01-01   -0.427644\n",
       "2001-01-02   -0.377475\n",
       "2001-01-03   -1.158527\n",
       "2001-01-04   -0.633258\n",
       "2001-01-05    0.805478\n",
       "2001-01-06   -1.078929\n",
       "2001-01-07    0.265215\n",
       "2001-01-08   -0.395753\n",
       "2001-01-09   -0.993741\n",
       "2001-01-10    3.162702\n",
       "Freq: D, dtype: float64"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.date_range('2001-01-01', periods=100, freq='D')\n",
    "ts = pd.Series(np.random.randn(len(rng)), index=rng)\n",
    "\n",
    "ts[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2001-01-31   -0.148010\n",
       "2001-02-28    0.007180\n",
       "2001-03-31    0.201887\n",
       "2001-04-30   -0.493140\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('M').mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2001-01   -0.148010\n",
       "2001-02    0.007180\n",
       "2001-03    0.201887\n",
       "2001-04   -0.493140\n",
       "Freq: M, dtype: float64"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('M', kind='period').mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Downsampling\n",
    "#### Aggregating data to regular, lower frequency is pretty normal task.\n",
    "#### The data you are aggregating does not need to be fixed frequently, the desired frequency defines 'bin edges' used to slice teh time series into pieces to aggregate.\n",
    "#### Each interval is said to be half-open, a data point can only be in one interval and a union of intervals must make up whole time frame.\n",
    "#### There are couple of things to think about before using 'resample' to downsample data:\n",
    "####     1. Which side of the interval is closed.\n",
    "####     2. How to label each aggregated bin, either with start of interval or the end."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01 00:00:00     0\n",
       "2000-01-01 00:01:00     1\n",
       "2000-01-01 00:02:00     2\n",
       "2000-01-01 00:03:00     3\n",
       "2000-01-01 00:04:00     4\n",
       "2000-01-01 00:05:00     5\n",
       "2000-01-01 00:06:00     6\n",
       "2000-01-01 00:07:00     7\n",
       "2000-01-01 00:08:00     8\n",
       "2000-01-01 00:09:00     9\n",
       "2000-01-01 00:10:00    10\n",
       "2000-01-01 00:11:00    11\n",
       "Freq: T, dtype: int32"
      ]
     },
     "execution_count": 151,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng = pd.date_range('2000-01-01', periods=12, freq='T')\n",
    "ts = pd.Series(np.arange(12), index=rng)\n",
    "ts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### We can aggregate any time series data into chunks or bars of defined frequency and use an aggregate function on them. eg - sum, avg, etc.\n",
    "#### The frequency you pass defines the bin edges. By default, the 'left' bin edge is inclusive. But passing \" closed='right' \" changes the interval to be closed on the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01 00:00:00    10\n",
       "2000-01-01 00:05:00    35\n",
       "2000-01-01 00:10:00    21\n",
       "Freq: 5T, dtype: int32"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('5min').sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1999-12-31 23:55:00     0\n",
       "2000-01-01 00:00:00    15\n",
       "2000-01-01 00:05:00    40\n",
       "2000-01-01 00:10:00    11\n",
       "Freq: 5T, dtype: int32"
      ]
     },
     "execution_count": 155,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('5min', closed='right').sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### By default, the series is labeled by timestamps from left side of each bin. You can make it the right edge of the bin by passing \" label='right' \".\n",
    "#### You may sometime want to shift the result by some amount (eg - subtract 1 second from right edge of bin). For this, you can pass a string or date offset to 'loffset'.\n",
    "#### You can achieve the same effect by calling the 'shift' method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2000-01-01 00:00:00     0\n",
       "2000-01-01 00:05:00    15\n",
       "2000-01-01 00:10:00    40\n",
       "2000-01-01 00:15:00    11\n",
       "Freq: 5T, dtype: int32"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('5min', closed='right', label='right').sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1999-12-31 23:59:59     0\n",
       "2000-01-01 00:04:59    15\n",
       "2000-01-01 00:09:59    40\n",
       "2000-01-01 00:14:59    11\n",
       "Freq: 5T, dtype: int32"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('5min', closed='right', \n",
    "            label='right', loffset='-1s').sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Open-High-Low-Close (OHLC) resampling:\n",
    "#### In finance, a popular way to aggregate time series is to compute 4 values for each bucket: first (open), last (close), maximum (high) and minimal (low) values.\n",
    "####     We can use the 'ohlc' aggregate function to get a DataFrame having columns having the 4 aggregates, which are efficiently computed is a single sweep of the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>open</th>\n",
       "      <th>high</th>\n",
       "      <th>low</th>\n",
       "      <th>close</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-01 00:00:00</th>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-01 00:05:00</th>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-01 00:10:00</th>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     open  high  low  close\n",
       "2000-01-01 00:00:00     0     4    0      4\n",
       "2000-01-01 00:05:00     5     9    5      9\n",
       "2000-01-01 00:10:00    10    11   10     11"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts.resample('5min').ohlc()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Upsampling and Interpolation\n",
    "#### When converting low frequency to higher frequency, we do not need aggergation.\n",
    "#### When we want to aggregate with only 1 value per group, then missing values result in gaps. We use 'asfreq' method to convert to the higher frequencies without aggregation.\n",
    "#### Next, we fill the gaps using filling or interpolation methods available like 'ffill', fillna' and 'reindex' which we used for resampling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>-1.352802</td>\n",
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       "      <th>2000-01-12</th>\n",
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      "text/plain": [
       "            Colorado     Texas  New York     Ohio\n",
       "2000-01-05 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-12  0.349695  0.435194 -0.174149 -0.65500"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.random.randn(2,4),\n",
    "                    index=pd.date_range('1/1/2000', periods=2,\n",
    "                                       freq='W-WED'),\n",
    "                    columns=['Colorado', 'Texas', 'New York', 'Ohio'])\n",
    "frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>2000-01-05</th>\n",
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       "      <th>2000-01-06</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
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       "    <tr>\n",
       "      <th>2000-01-08</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-09</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-12</th>\n",
       "      <td>0.349695</td>\n",
       "      <td>0.435194</td>\n",
       "      <td>-0.174149</td>\n",
       "      <td>-0.65500</td>\n",
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      ],
      "text/plain": [
       "            Colorado     Texas  New York     Ohio\n",
       "2000-01-05 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-06       NaN       NaN       NaN      NaN\n",
       "2000-01-07       NaN       NaN       NaN      NaN\n",
       "2000-01-08       NaN       NaN       NaN      NaN\n",
       "2000-01-09       NaN       NaN       NaN      NaN\n",
       "2000-01-10       NaN       NaN       NaN      NaN\n",
       "2000-01-11       NaN       NaN       NaN      NaN\n",
       "2000-01-12  0.349695  0.435194 -0.174149 -0.65500"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_daily = frame.resample('D').asfreq()\n",
    "df_daily"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
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       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
       "      <td>0.879472</td>\n",
       "      <td>0.19245</td>\n",
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       "    <tr>\n",
       "      <th>2000-01-10</th>\n",
       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
       "      <td>0.879472</td>\n",
       "      <td>0.19245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-11</th>\n",
       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
       "      <td>0.879472</td>\n",
       "      <td>0.19245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-12</th>\n",
       "      <td>0.349695</td>\n",
       "      <td>0.435194</td>\n",
       "      <td>-0.174149</td>\n",
       "      <td>-0.65500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Colorado     Texas  New York     Ohio\n",
       "2000-01-05 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-06 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-07 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-08 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-09 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-10 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-11 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-12  0.349695  0.435194 -0.174149 -0.65500"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame.resample('D').ffill()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### You can similarly choose to only fill certain number of periods to limit how far to conyinue without an observed value.\n",
    "#### The new date index created need not overlap the old one at all. If we resample back with the same frequency, we will get the original series back."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-05</th>\n",
       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
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       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
       "      <td>0.879472</td>\n",
       "      <td>0.19245</td>\n",
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       "    <tr>\n",
       "      <th>2000-01-07</th>\n",
       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
       "      <td>0.879472</td>\n",
       "      <td>0.19245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-08</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-09</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-10</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-11</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-12</th>\n",
       "      <td>0.349695</td>\n",
       "      <td>0.435194</td>\n",
       "      <td>-0.174149</td>\n",
       "      <td>-0.65500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Colorado     Texas  New York     Ohio\n",
       "2000-01-05 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-06 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-07 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-08       NaN       NaN       NaN      NaN\n",
       "2000-01-09       NaN       NaN       NaN      NaN\n",
       "2000-01-10       NaN       NaN       NaN      NaN\n",
       "2000-01-11       NaN       NaN       NaN      NaN\n",
       "2000-01-12  0.349695  0.435194 -0.174149 -0.65500"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame.resample('D').ffill(limit=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01-06</th>\n",
       "      <td>-1.352802</td>\n",
       "      <td>0.371774</td>\n",
       "      <td>0.879472</td>\n",
       "      <td>0.19245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-01-13</th>\n",
       "      <td>0.349695</td>\n",
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      ],
      "text/plain": [
       "            Colorado     Texas  New York     Ohio\n",
       "2000-01-06 -1.352802  0.371774  0.879472  0.19245\n",
       "2000-01-13  0.349695  0.435194 -0.174149 -0.65500"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Old time series can be attained without overlap.\n",
    "frame.resample('W-THU').ffill()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resampling with Periods\n",
    "#### Resampling data indexed by periods is similar to timestamps.\n",
    "#### Upsampling is more nuanced, as you have to make a decision about which end of the timespan in the new frequency to place the values before resampling. Just like 'asfreq' method. \n",
    "#### The 'convention' argument defaults to 'start' but you can change it to 'end'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000-01</th>\n",
       "      <td>-0.249231</td>\n",
       "      <td>-2.065552</td>\n",
       "      <td>-0.604521</td>\n",
       "      <td>-0.078377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-02</th>\n",
       "      <td>-0.987753</td>\n",
       "      <td>-0.318903</td>\n",
       "      <td>0.311977</td>\n",
       "      <td>0.091783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-03</th>\n",
       "      <td>0.298468</td>\n",
       "      <td>0.803729</td>\n",
       "      <td>-0.623903</td>\n",
       "      <td>1.369662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-04</th>\n",
       "      <td>0.458932</td>\n",
       "      <td>0.406961</td>\n",
       "      <td>-0.276269</td>\n",
       "      <td>1.158306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-05</th>\n",
       "      <td>-0.427215</td>\n",
       "      <td>0.140441</td>\n",
       "      <td>0.264665</td>\n",
       "      <td>1.763246</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Colorado     Texas  New York      Ohio\n",
       "2000-01 -0.249231 -2.065552 -0.604521 -0.078377\n",
       "2000-02 -0.987753 -0.318903  0.311977  0.091783\n",
       "2000-03  0.298468  0.803729 -0.623903  1.369662\n",
       "2000-04  0.458932  0.406961 -0.276269  1.158306\n",
       "2000-05 -0.427215  0.140441  0.264665  1.763246"
      ]
     },
     "execution_count": 169,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame = pd.DataFrame(np.random.randn(24, 4),\n",
    "                    index=pd.period_range('1-2000', '12-2001',\n",
    "                                         freq='M'),\n",
    "                    columns=['Colorado', 'Texas', 'New York', 'Ohio'])\n",
    "\n",
    "frame[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
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       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Colorado     Texas  New York      Ohio\n",
       "2000 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001  0.058988 -0.262638 -0.173303  0.317646"
      ]
     },
     "execution_count": 170,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_frame = frame.resample('A-DEC').mean()\n",
    "\n",
    "annual_frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000Q1</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000Q2</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000Q3</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000Q4</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q1</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q2</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q3</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q4</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Colorado     Texas  New York      Ohio\n",
       "2000Q1 -0.102447 -0.043813  0.077324  0.562220\n",
       "2000Q2 -0.102447 -0.043813  0.077324  0.562220\n",
       "2000Q3 -0.102447 -0.043813  0.077324  0.562220\n",
       "2000Q4 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q1  0.058988 -0.262638 -0.173303  0.317646\n",
       "2001Q2  0.058988 -0.262638 -0.173303  0.317646\n",
       "2001Q3  0.058988 -0.262638 -0.173303  0.317646\n",
       "2001Q4  0.058988 -0.262638 -0.173303  0.317646"
      ]
     },
     "execution_count": 171,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Q-DEC: Quarterly, year ending in December\n",
    "annual_frame.resample('Q-DEC').ffill()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000Q4</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q1</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q2</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q3</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q4</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Colorado     Texas  New York      Ohio\n",
       "2000Q4 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q1 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q2 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q3 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q4  0.058988 -0.262638 -0.173303  0.317646"
      ]
     },
     "execution_count": 172,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_frame.resample('Q-DEC', convention='end').ffill()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Periods refer to timespans, teh rules about upsampling and downsampling are a more rigid:\n",
    "####     1. In downsampling, target frequency must be a 'subperiod' of source frequency.\n",
    "####     2. In upsampling, target frequency must be a 'superperiod' of source frequency.\n",
    "#### If the above rules are not satisfied , an exception will be raised. This mainly affects quarterly, annual and weekly frequencies.\n",
    "#### eg - timespans defined by 'Q-MAR' only line up with 'A-MAR', 'A-JUN', 'A-SEP' and 'A-DEC'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Colorado</th>\n",
       "      <th>Texas</th>\n",
       "      <th>New York</th>\n",
       "      <th>Ohio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2000Q4</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q1</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q2</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q3</th>\n",
       "      <td>-0.102447</td>\n",
       "      <td>-0.043813</td>\n",
       "      <td>0.077324</td>\n",
       "      <td>0.562220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001Q4</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002Q1</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002Q2</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002Q3</th>\n",
       "      <td>0.058988</td>\n",
       "      <td>-0.262638</td>\n",
       "      <td>-0.173303</td>\n",
       "      <td>0.317646</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Colorado     Texas  New York      Ohio\n",
       "2000Q4 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q1 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q2 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q3 -0.102447 -0.043813  0.077324  0.562220\n",
       "2001Q4  0.058988 -0.262638 -0.173303  0.317646\n",
       "2002Q1  0.058988 -0.262638 -0.173303  0.317646\n",
       "2002Q2  0.058988 -0.262638 -0.173303  0.317646\n",
       "2002Q3  0.058988 -0.262638 -0.173303  0.317646"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "annual_frame.resample('Q-MAR').ffill()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Moving window Functions\n",
    "#### An important class of array transformations used for time series operations are staistics and other functions evaluated over sliding window or exponentially decaying weights.\n",
    "#### It can be useful for smoothing noisy or gappy data. We cam call these 'moving window functions' although they also include exponentially weighted moving average.\n",
    "#### These functions can authomatically exclude missing data like other statistical functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 176,
   "metadata": {},
   "outputs": [],
   "source": [
    "close_px_all = pd.read_csv('examples/stock_px_2.csv',\n",
    "                          parse_dates=True, index_col=0)\n",
    "\n",
    "close_px = close_px_all[['AAPL', 'MSFT', 'XOM']]\n",
    "\n",
    "close_px = close_px.resample('B').ffill()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The first method we will look into is the 'rolling' operator, which behaves similarly to 'resample' and 'groupby'.\n",
    "#### It can be called on a Series and DataFrame with a 'window' with number of periods.\n",
    "#### Its behavior is similar to 'groupby' but instead of grouping, it creates object that enables grouping over the specified sliding window.\n",
    "#### By default, it requires all values in the window to be non-NA, but this can be changed to account for missing data, especially if you have fewer data that the window period."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x2584229bbe0>"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "close_px.AAPL.plot()\n",
    "close_px.AAPL.rolling(250).mean().plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2003-01-09         NaN\n",
       "2003-01-10         NaN\n",
       "2003-01-13         NaN\n",
       "2003-01-14         NaN\n",
       "2003-01-15    0.077496\n",
       "2003-01-16    0.074760\n",
       "2003-01-17    0.112368\n",
       "Freq: B, Name: AAPL, dtype: float64"
      ]
     },
     "execution_count": 181,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We are accounting for minimum of 10 NA values in a window\n",
    "aapl_std250 = close_px.AAPL.rolling(250, min_periods=10).std()\n",
    "\n",
    "aapl_std250[5:12]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x25842232d68>"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aapl_std250.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Another variation to window is expanding window, which starts at the beginning of the series and increases its size until it encompasses the whole series.\n",
    "#### For this feature we use the 'expanding' operator and then aggregator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x258423d7ba8>"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MH/19JT95fjVj+3XlzZtP4xvj+qrwy1HVdRDwceDcastuAd5x9yHAO6HHX2BmScDtwHggHbi9tl8SIlJ/O/YVcNEDHzF/xS5+cNYQnp4xnu6d2gYdS5qBOhV/d38f2F9t8YXAE6H7TwAX1fDUrwBvu/t+dz8AvM1//hIRkQb4eMteLnzgI3IPF/P09PH88Oyhmmhd6iycMf8e7p4N4O7ZZta9hjZ9gMwqj7NCy0QkDM8s3sHtL61jQHIij05Lo3+3xKAjSTPT2F/41rQb4jU2NJsJzARITU1tzEwizVZZeQV3vbaBxz/ezunDUrjv8rF0ats66FjSDIVz4O8eM+sFEPqZU0ObLKDqLNB9gd01debus9w9zd3TUlJSwogl0jIdKSnj208t4/GPtzNj8kAenXayCr80WDjF/2Xg86N3pgEv1dDmTeAcM+sa+qL3nNAyEamH3Pxips5axLubcvj1RSP5xXnDNb4vYanTsI+ZzQVOB5LNLIvKI3juBv5uZtOBncAlobZpwA3uPsPd95vZr4Gloa7udPfqXxyLyFFkHTjCFQ8vJie/iIeuSuPs4T2CjiQtgLnXOAQfqLS0NM/IyAg6hkjgdh0s5LKHFnKosJQnrktnbKqOlJaamdkyd0+ra3ud4SsSpfYdLuaKhxeRV1jKMzPGM6pvl6AjSQuiKz2JRKHisnJueHoZn+UV8fi16Sr8EnHa8xeJMu7OrS+uZen2A/zl8rGM66+hHok87fmLRJk5S3bywvIsbv7yEM4f3TvoONJCqfiLRJEN2Yf4r1fWc9rQFG46c0jQcaQFU/EXiRJHSsr43pzldGnXmj9eOpo4HccvjUhj/iJR4n/e/oStuQXMuX48yR3aBB1HWjjt+YtEgXW785j90XYuT09l4nHJQceRGKDiLxKw8grn1vlr6dq+Nbece3zQcSRGqPiLBOyZxTtYlXmQX543nM7tdaE2aRoq/iIB2nOoiN+/sYlThyRzgQ7rlCak4i8SoDtfWU9xeQW/vnCk5tyVJqXiLxKQdzfm8NqabG46czADkjUTlzQtFX+RABwpKeOXL61lcPcOzDztuKDjSAzScf4iAfjjW5+QdaCQ5244hYRW2geTpqd3nUgTW5V5kNkfbeNbE1I5eUBS0HEkRqn4izSh0vIKfvbCalI6tuGnOqZfAqRhH5Em9NB7W9j4WT6zrhqnydclUA3e8zezYWa2ssrtkJndXK3N6WaWV6XNr8KPLNI8rcnK40//3Mx5o3pxzoieQceRGNfgPX933wSMATCzeGAXML+Gph+4+3kN3Y5IS1BYUs7Nz64guUMbfnPRiUHHEYnYsM9ZwBZ33xGh/kRalLtf38CW3AKemTFel3CQqBCpL3ynAnNrWXeKma0ys9fNbERtHZjZTDPLMLOM3NzcCMUSCd5LK3fxxMIdTJ88kEmDdcVOiQ5hF38zSwAuAJ6rYfVyoL+7jwb+Avyjtn7cfZa7p7l7WkpKSrixRKLCmqw8fvbCatIHJPEzHd0jUSQSe/5fBZa7+57qK9z9kLsfDt1fALQ2M+36SEzY9Fk+V89eTLfENjxw5Uk6mUuiSiTejZdTy5CPmfW00NWqzCw9tL19EdimSFTbvCefbz26mIRWccy5fjwpHTUzl0SXsL7wNbP2wNnAt6ssuwHA3R8Evgl8x8zKgEJgqrt7ONsUiXYZ2/cz/YkMElrF8cyMCfTvpou2SfQJq/i7+xGgW7VlD1a5fz9wfzjbEGlO3lz3GTfNXUGfru144tp0+iW1DzqSSI10hq9IhDy9aAe/emkto/p2YfY1J5OUmBB0JJFaqfiLhKmiwrnnjY089P5Wzjy+O/dfMZb2CfpoSXTTO1QkDJ+fufvmuj1cNaE/t58/nFbxOqpHop+Kv0gDbck9zE1zV7A++xC/Om84104aoKkYpdlQ8RepJ3dn7pJMfv3qetq2juPRaWmceXyPoGOJ1IuKv0g9bN9bwM9fXMPCrfuYNLgbf7x0DD06tQ06lki9qfiL1MHh4jIe+WArf/vfLSTEx/Hbi0/ksrR+xMVpmEeaJxV/kaMoKi3n2aWZ/OVfm9l7uISvndiLX543nJ6dtbcvzZuKv0gN9h0u5qlFO3hy4Q72F5SQPjCJh68+nrGpXYOOJhIRKv4iVWz87BBPLdzB88uyKC6r4MsndOf6UweRPjBJR/JIi6LiLzGvqLScV1dnM2fxDpbvPEhCqzguHtuHGacOZHD3jkHHE2kUKv4Sk9ydDdn5/D0jkxeXZ3GoqIxBKYn84msn8I2T+tJVl2aQFk7FX2JGRYWzZlce72zYw6trstmaW0DreOPckb24Ij2VCYM0tCOxQ8VfWpyi0nJ2HSwk60AhWQeOkLm/kJ37C1i8dT/7CkqIMxg/sBvTJw/kqyN76QJsEpNU/KXZKiwpZ2XmQVZlHWRbbgHb9hawfV8BOfnFX2jXOt7o3aUdk4ckc/qwFE4bkkK3DppcRWKbir80K4eKSnljzWe8uiabhVv2UlpeOTdQcoc2DExuz2lDU0hNak/fru3o27U9/ZLa0b1jW+J1MpbIF6j4S7Ow62AhD7+/lecyMikoKSc1qT3XThrIhEFJnJTalS7tNXQjUh8q/hLVCkvK+ev/fsqs97dS4c55o3ozbeIARvftrC9nRcIQdvE3s+1APlAOlLl7WrX1BvwZmAIcAa5x9+XhbldavrW78rhp3gq25hZwweje/Oyrx9OnS7ugY4m0CJHa8z/D3ffWsu6rwJDQbTzwt9BPkRq5O7M/2s7dr28gKTGBZ2aMZ9Lg5KBjibQoTTHscyHwpLs7sMjMuphZL3fPboJtSzNTVFrOrfPX8OLyXZw9vAe/+8YonXAl0ggiUfwdeMvMHHjI3WdVW98HyKzyOCu07AvF38xmAjMBUlNTIxBLmpu9h4uZ+WQGy3ce5IdfHspNZw3WuL5II4lE8Z/k7rvNrDvwtpltdPf3q6yv6dPr/7Gg8pfGLIC0tLT/WC8t255DRVzx8CJ2HSzkr1eexJQTewUdSaRFC3umaXffHfqZA8wH0qs1yQL6VXncF9gd7nal5cg6cIRLH1rIZ3lFPHFtugq/SBMIq/ibWaKZdfz8PnAOsLZas5eBq63SBCBP4/3yue17C7j0wYUcKCjh6RnjGT+oW9CRRGJCuMM+PYD5oXHZVsAcd3/DzG4AcPcHgQVUHub5KZWHel4b5jalhdi8J58rH1lMWYUzd+YERvTuHHQkkZgRVvF3963A6BqWP1jlvgPfC2c70vKs253HVY8uIT7OmDdzAkN76Lr5Ik1JZ/hKk1uZeZBps5eQmBDPM9dPYGByYtCRRGKOir80qaXb93PtY0vpmtiaOTMm0C+pfdCRRGKSir80mfc+yeWGp5bRq0tb5syYQM/ObYOOJBKzVPyl0bk7s97fyj1vbGRoj448NX08KR11PX2RIKn4S6PKzS/m1vlreHv9Hr52Yi9+f8ko2ifobScSNH0KpVEUl5Uzb0kmf/rnJxSUlPOLr53A9MkDdbkGkSih4i8R4+6s3XWI+St28crq3eTmFzN+YBJ3XTSSITqUUySqqPhL2DL3H+EfK3Yxf+UutuYWkBAfx+nDUrjqlP5MHpysvX2RKKTiLw1SWl7Ba6uzmbNkJ0u27QcgfWAS1586iCkje9G5feuAE4rI0aj4S72UlVcwd8lOHnxvK7sOFjIwOZEfnzOUi8b2oW9XHbMv0lyo+Eudfbh5L//1yjo25xxmXP+u3HnhCM4Y1p24OA3riDQ3Kv5yTEdKyvjvBRt4etFO+ndrz0NXjeOc4T00li/SjKn4y1F9siefG55axta9BcyYPJAff2UYbVvHBx1LRMKk4i+1+tfGPdw0dyVtW8czZ8Z4JmoSdZEWQ8VfavTYR9u489X1DO/ViYevTqN3l3ZBRxKRCFLxly9wd/78zmb+9M/NfGVED/7nsjG6HINIC6RPtfybu3PXaxt49MNtfHNcX+6++ERaxYc9zbOIRKEGf7LNrJ+ZvWtmG8xsnZn9oIY2p5tZnpmtDN1+FV5caSzuzn8vqCz810wcwO++MUqFX6QFC2fPvwz4f+6+PDSJ+zIze9vd11dr94G7nxfGdqQJ/O29LTz8wTamndKf288frsM4RVq4Bu/auXu2uy8P3c8HNgB9IhVMms7cJTv53RubuGB0b24/f4QKv0gMiMjf9WY2ABgLLK5h9SlmtsrMXjezEZHYnkTOgjXZ3DZ/DacPS+HeS0frbF2RGBH2F75m1gF4AbjZ3Q9VW70c6O/uh81sCvAPYEgt/cwEZgKkpqaGG0vq4MPNe7l53kpOSu3K364cR2uN8YvEjLA+7WbWmsrC/4y7v1h9vbsfcvfDofsLgNZmVuOZQu4+y93T3D0tJSUlnFhSB6syDzLzqQwGpSTy6LSTaZegs3ZFYkk4R/sY8Ciwwd3/WEubnqF2mFl6aHv7GrpNiYxPcw5zzWNLSEpM4Inr0nX5ZZEYFM6wzyTgKmCNma0MLbsVSAVw9weBbwLfMbMyoBCY6u4exjYlTNl5hUybvYT4OOPp6ePp0alt0JFEJAANLv7u/iFw1G8H3f1+4P6GbkMiK+vAEa58ZDF5haXMmzmBAcmJQUcSkYDoDN8YsTX3MN96ZDGHi8t4cno6I/t0DjqSiARIxT8GZGzfz7efWoYDc2dOYERvFX6RWKdj+1q45zIyufzhRXRs24rnbjhFhV9EAO35t1glZRXc/fpGZn+0jUmDu/HAFSfRpX1C0LFEJEqo+LdAO/YV8P25K1idlcc1Ewdw29dO0AlcIvIFKv4tSElZBY9+uI373tlMQqs4Zl01jnNG9Aw6lohEIRX/FiA3v5gXlmfx2Efb2HOomHOG9+COC0Zo9i0RqZWKfzPj7mTnFbEq8yArMw+SseMAy3cewB0mDe7GvZeMYfIQzbUrIken4h+FSsoq2F9QQm5+Mdv2FbAtt4Ctew+zbW/l/fziMgAS4uM4oXcnfnDWEKac2IuhPToGnFxEmgsV/yZSXFbO7oNFZB04wp5DxRwoKOHAkRIOHCnlQEEJ+wqK2Xe4hL2HizlUVPaF55pB787tGJSSyMUn9WFQSgdG9e3M8N6daNNKF2QTkfpT8Y+wigpnc85h1u3OY0P2IdZnH+LTnMPsOVT8H21bxRld2ieQlNiaboltGN67E90SE+jWoQ3dOiTQLbENA5LbM6BbIm1bq8iLSOSo+EfAzn1H+OeGPSzauo/F2/aTV1gKQEKrOIb16MjkwSmkJrWnb9d29O3ajp6d29I1MYGObVpp1iwRCYSKfwNt21vAgjXZLFiTzbrdlXPYpCa15ysjepA+sBuj+nZmUHKiJkEXkaik4l8PR0rKeHV1Ns8uzWTZjgMAjE3twm1TTuDckT3pl9Q+4IQiInWj4n8M7s7qrDzmLc3klVW7OVxcxnEpidw65XjOG9Vbx9KLSLOk4l+LvCOlzF+RxbylmWz8LJ+2reM4b1Rvpp7cj3H9u2qsXkSaNRX/KtydRVv38+zSnSxY+xklZRWc2Kczv/n6SM4f3ZtObTXdoYi0DCr+QM6hIp5fnsXfl2ayfd8ROrZtxdST+3FpWj9NeiIiLVJYxd/MzgX+DMQDj7j73dXWtwGeBMZROXH7Ze6+PZxtRkpJWQUfbM5l3tJM/rUxh/IKZ/zAJH7w5SF8dWQvHVcvIi1ag4u/mcUDDwBnA1nAUjN72d3XV2k2HTjg7oPNbCpwD3BZOIGPpqLCeX5ZFou27eNQYRkl5RWUlJVTUlYRuv9/t4OFpRwpKSe5QwIzTh3IZWn9GJTSobGiiYhElXD2/NOBT919K4CZzQMuBKoW/wuBO0L3nwfuNzNzdw9ju7WafM+/2J1XRPeObUju0IaEVnEktIojsU0rusTHkRAf9+9lHdq0YtLgZE4flqJr3YtIzAmn+PcBMqs8zgLG19bG3cvMLA/oBuwNY7s1qqhwJg1O5uSBSVwyrq+OxhEROYpwin9N1bX6Hn1d2lQ2NJsJzARITU2td5i4OOP3l4yu9/NERGJROOMdWUC/Ko/7Artra2NmrYDOwP6aOnP3We6e5u5pKSkpYcQSEZFjCaf4LwWGmNlAM0sApgIvV2vzMjAtdP+bwL8aa7xfRETqrsHDPqE+ZFkkAAAGD0lEQVQx/BuBN6k81HO2u68zszuBDHd/GXgUeMrMPqVyj39qJEKLiEh4wjrO390XAAuqLftVlftFwCXhbENERCJPxziKiMQgFX8RkRik4i8iEoNU/EVEYlDUXdUzdLLXXjPbUW1VZyDvKE9N5thnDh+rj7q0qUsfLS1LJLI2tyyR2k60vG+jKYveK42TZdgxnvtF7h5VNyoPE61p+ayGPK8+fdRxO3Xpo0VliUTW5pYlgtuJivdtNGXRe6VxstTlNat6a07DPq80UR/HahOJHHXtJ1qyRCJrXUVLlkhtR1kaJ0ekthMtr0ld20SMhX5jRA0zy3D3tKZ6XmNQlpopS/TmAGWpTXPJUt+c0bjnP6uJn9cYlKVmyvKfoiUHKEttmkuWeuWMuj1/ERFpfNG45y8iIo0sqou/mfUzs3fNbIOZrTOzH4SWJ5nZ22a2OfSza2i5mdl9Zvapma02s5NCy/ub2TIzWxnq54YgclTpr5OZ7TKz+4N6TULrykOvyUozq35F1qbOkmpmb4X6Wm9mA4LIYmZnVHlNVppZkZldFODr8rtQHxtCbeo8S1GEc9xjZmtDt3pPxdqALMeb2UIzKzazH1fr61wz2xTKeUvAWWabWY6Zra1vjkhmqa2fo6rPoUFNfQN6ASeF7ncEPgGGA78DbgktvwW4J3R/CvA6lZPITAAWh5YnAG1C9zsA24HeTZ2jSn9/BuYA9wf1moTWHY6G/5/Quv8Fzq7yf9Q+qCxV+kyi8mq0gWQBJgIfUXnV3HhgIXB6ADm+BrxN5XlBiUAG0KmRX5PuwMnAb4AfV+knHtgCDKLyc70KGB5EltC604CTgLVN9Bmq7XWpsZ+jbjucD39T34CXqJwwfhPQq8o/elPo/kPA5VXa/7tdlWXdgJ3Uo/hHMgcwDpgHXEMDin+Es4RV/COVJfRm/zAaslTrYybwTICvyynAMqAd0J7KontCADl+AvyiyvJHgUsb8zWp0u4OvljkTgHerPL458DPg8hSZfkAGlj8I52lej9H21ZUD/tUFRoGGAssBnq4ezZA6Gf3ULOa5hXuE3p+PzNbHVp/j7tXn3Ws0XOYWRxwL5UfprCF+5oAbc0sw8wW1XdoI8JZhgIHzexFM1thZr83s/iAslQ1FZjb0BzhZnH3hcC7QHbo9qa7b2jqHFTuXX/VzNqbWTJwBl+cxa8xstSmLv9vTZUloiKVpVo/tWoWxd/MOgAvADe7+6GjNa1hmQO4e6a7jwIGA9PMrEcAOb4LLHD3zBrWN3UWgFSvPC74CuBPZnZcQFlaAacCP6byT9pBVP5lFESWz/vpBZxI5WRFDRJuFjMbDJxA5RSpfYAzzey0ps7h7m9ROW/Hx1T+MlwIlNU3Rz2z1CtjQFkiJlJZ6tNP1Bd/M2tN5T/mGXd/MbR4T+jD+fmHNCe0/JjzCof2+NdRWWyaOscpwI1mth34A3C1md1dnxwRzPL5a4G7b6VyzH1sQFmygBXuvtXdy4B/UDmOGkSWz10KzHf30vrmiGCWrwOL3P2wux+mcjx+QgA5cPffuPsYdz+bygK8uT45GpClNnWZO7ypskREpLLU0k+torr4m5lROb64wd3/WGVV1bmBp1E5vvX58qut0gQgz92zzayvmbUL9dkVmETlmFqT5nD3K9091d0HULmX+6S71+tohQi+Jl3NrE2oz2QqX5P1QWShcj7ormaWEmp3ZoBZPnc5DRzyiWCWncCXzKxV6IP9JaDOwz4RfK/Em1m3UJ+jgFHAW3XN0cAstanL3OFNlSVskcpylH5qF4kvKRrrBkym8k+61cDK0G0KlV/avkPl3sc7QFKovQEPUHk0wBogLbT87FAfq0I/ZwaRo1qf19Cwo30i9ZpMDD1eFfo5Pags1f6P1gCPAwkBZhkA7ALiAn7fxlP5JewGKn8Z/jGgHG1D218PLALGNMFr0pPKvfxDwMHQ/U6hdVOoPJplC3BbwFnmUvl9TGloeb0+R5HKUls/R9u2zvAVEYlBUT3sIyIijUPFX0QkBqn4i4jEIBV/EZEYpOIvIhKDVPxFRGKQir+ISAxS8RcRiUH/H6aK4Vbg1EfPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expanding_mean = aapl_std250.expanding().mean()\n",
    "expanding_mean.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calling a window on a DataFrame applies transformation to each column.\n",
    "#### The rolling function also accepts a string which indicates a fixed-size time offset, rather than set number of periods.\n",
    "#### This can be useful for irregular time series. The same strings can be used in 'resample'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x258433c9710>"
      ]
     },
     "execution_count": 190,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "close_px.rolling(60).mean().plot(logy=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AAPL</th>\n",
       "      <th>MSFT</th>\n",
       "      <th>XOM</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2003-01-02</th>\n",
       "      <td>7.400000</td>\n",
       "      <td>21.110000</td>\n",
       "      <td>29.220000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-03</th>\n",
       "      <td>7.425000</td>\n",
       "      <td>21.125000</td>\n",
       "      <td>29.230000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-06</th>\n",
       "      <td>7.433333</td>\n",
       "      <td>21.256667</td>\n",
       "      <td>29.473333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-07</th>\n",
       "      <td>7.432500</td>\n",
       "      <td>21.425000</td>\n",
       "      <td>29.342500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-08</th>\n",
       "      <td>7.402000</td>\n",
       "      <td>21.402000</td>\n",
       "      <td>29.240000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-09</th>\n",
       "      <td>7.391667</td>\n",
       "      <td>21.490000</td>\n",
       "      <td>29.273333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-10</th>\n",
       "      <td>7.387143</td>\n",
       "      <td>21.558571</td>\n",
       "      <td>29.238571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-13</th>\n",
       "      <td>7.378750</td>\n",
       "      <td>21.633750</td>\n",
       "      <td>29.197500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-14</th>\n",
       "      <td>7.370000</td>\n",
       "      <td>21.717778</td>\n",
       "      <td>29.194444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-01-15</th>\n",
       "      <td>7.355000</td>\n",
       "      <td>21.757000</td>\n",
       "      <td>29.152000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                AAPL       MSFT        XOM\n",
       "2003-01-02  7.400000  21.110000  29.220000\n",
       "2003-01-03  7.425000  21.125000  29.230000\n",
       "2003-01-06  7.433333  21.256667  29.473333\n",
       "2003-01-07  7.432500  21.425000  29.342500\n",
       "2003-01-08  7.402000  21.402000  29.240000\n",
       "2003-01-09  7.391667  21.490000  29.273333\n",
       "2003-01-10  7.387143  21.558571  29.238571\n",
       "2003-01-13  7.378750  21.633750  29.197500\n",
       "2003-01-14  7.370000  21.717778  29.194444\n",
       "2003-01-15  7.355000  21.757000  29.152000"
      ]
     },
     "execution_count": 191,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Instead of fixed time period, we have a set number of days (20 days) as window\n",
    "close_px.rolling('20D').mean().head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exponentially weighted functions\n",
    "#### Alternative to static window size with equally weighted observations is to specify a 'decay factor', giving more weight to recent observations.\n",
    "#### There are couple of ways to specify decay factor. Most popular one is using 'span'. Its result is comparable to simple moving window with window size equal to span.\n",
    "#### Because exponentially weighted statistics places more weights on recent observations, it 'adapts' more quickly to changes.\n",
    "#### pandas has 'ewm' (Exponentially Weighted Moving) operator to go with 'rolling' and 'expanding'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x25843aef470>"
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "aapl_px = close_px.AAPL['2006':'2007']\n",
    "ma60 = aapl_px.rolling(30, min_periods=20).mean()\n",
    "\n",
    "ewma60 = aapl_px.ewm(span=30).mean()\n",
    "\n",
    "# Simple Moving Average. changes shown will be slower and inconspicuous.\n",
    "ma60.plot(style='k--', label='simple MA')\n",
    "\n",
    "# Expo weighted Moving Average. Changes shown will be quick and pronounced.\n",
    "ewma60.plot(style='k-', label='EW MA')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binary Moving Window\n",
    "#### For statistical operations (eg - covariance, correlation), we need to work on 2 time series.\n",
    "#### To get this, we first compute percent change for our entire time series of interest.\n",
    "#### The we can call 'corr' aggregation after 'rolling' to get rolling correlation between the two percent changes series.\n",
    "#### for finding correlation between multiple time series (eg - correlation between S&P 500 with different company stocks), we can write a loop and creating a new DataFrame of correlations. But this might be repetative.\n",
    "#### So instead we can pass a Series and a DataFrame to 'rolling_corr', which will compute correlation of the Series with each column of the DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x25843bbb7f0>"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "spx_px = close_px_all['SPX']\n",
    "spx_rets = spx_px.pct_change()\n",
    "returns = close_px.pct_change()\n",
    "\n",
    "corr = returns.AAPL.rolling(125, min_periods=100).corr(spx_rets)\n",
    "corr.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x25843c932e8>"
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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WtLlGuMDHRcBLUsrOwKnAq0JEfhJSyuellKOklKMKCgrCD8fHwHOg82hTA0ILhB438oPtVEqbBmCVM2gq6e50umd1j9h/af9LOb/f+fxw8Q/cMuqWJr3urbNXqOeXqxlttqbBuBsaN2CDnpPU/3H+dg7VHKLCWxFV56Y58Aa8uByuJodrwslKysIv/Qx9ZSg3fnFjQq6pSQ2HKxXS8uo/uZmJx8gXAl0sjzsTGY75FTALQEq5CEgBmq81enIWeHXJUF/YgkmqvnoeNu20samLRHuj4d7mzJNmctuxtwEqB31CpwkAvLPpnUZd/6SBSvjKn1RCZkDD9euvISV2aCUu8vTU0QamID+74tmQx7sqdjFvxzy+Lvy6aeMJwxPwkOpMfGPszpmmXs/8nfMTck0NcDgOj1rTeEaxGOgjhOgB7AYuBC4OO2cncCLwkhCiP8rINzIeEwfuVBWHB7Cu7p/yqPlFf/fXMPTCZhuCzdGDJrWEN8kwMkHuHns3Ock5EY0teuaorB0jbbOh9MxX8ffqlCJSkKoIqqnk6kZ+29fQcXjcT/NrfgJaAKdegHXqO2Zy3YLzFiCEQJNaiDxwY6jx10TqsyeAk7qdVP9JDSSAPGyE7OodhZTSD1wLzAXWobJo1gghHhBCnKmfdjNwlRBiBfA68AsZS7M1ESRnqioyKc10ycyOMHJGMDuApAx13MamHhbuXhg0yrcfG5Eh3Ci6ZnYFYFyncZzUPboRmdJlSqPDNQHju+3wMcTjhewudT+hHh7+dD39n9ygHnz9twY/f0vZlqj7p8yewuRZkzlxdsPi/SFICXPuYE/xhqhVx01FCBGS/hpL3qIhSCSORgqpJZq4bjVSyk+klH2llL2klA/q++6RUn6gb6+VUo6TUg6VUg6TUn7WnIOm3UCoKVbFT/9U017OexFcyaqc+5RHlA7HD/9s1mHYHB38dEBVeT4+6XEu6X9JQq75lwl/4bETHqNTRuwCmFR3KlW+xnUqCmjKyAeERmfN0eQ87Oe+2kINKRTKfALp8Xnc1urRZ5c/W8eZCiPds8F4yuH7Zzi0b0VINXIisS66frv72yZfLwA4WjE33srhMYqGktNN/a93mweg61hze+hF6v85t7XcmGyOaJzCGVO2oDFkJmVycveT6zzH7XA32ms0jLwmJM4Exn7nBEbjL94JWv2ZJs+c+AzjOo4DiEtb/ref/7Zxg9KTK6qRZBRtNZMttID69+O/VMV7E7BWNl+74NomXSsoicwR5MkfdrTpFfq4R1gbLSMunxq9hNnGxkpRTRF5KXktHkN1Cmej0/aMcI0mJK4mpHyGs0V2JBmPmb1WB6Pbj+a5qc+p7JQoN6s+uX1CHg/Jb2SKp+ZHArvdLtL3rYZ9q6B8LzyQBy+dDp/cAj82bdZ+73H38tTkp5p0jeBwDY2dIyUmf1jSbiCcaFYacvY/Is/pcxLkdG25MdkcsWwv306H9MZXnTYWl8MV7HbUUDTDkweczgQaeU33yA9FD60Yr2vFKZzBv2NL6RYKUgvIS8nj7TPeDp6TnZzdeEnfgJcNSepvzA5osPY9ePwYdWznd+r/Lx6K/fwlLypvvw7S3GlM7tqARit1EPTkG6oE2kwcmUYe4LhrYNSvVLd5S8uyIK5k8Lds5xqbI5PCikJ65/aO72QtEJm220gcwtHocI1fk4CGFOByJDV5LO2ykumQnUKRUbheHZkrf9UrS+h5xycR+x3CQUAG2FSyibPfP5uDNQc5vuPxCCH4/uLv+f7i78lwZwQXtxtM1SEq9fj2yNpaWPhE5DmxsqMCPvjoRuXth9fUROFnXRur/WOSCCG1RHJ4jKIxuJLh9MdVt/loOJNV5Suo+OLqd+L6kG3+t9CkRnFtMW1S4myy8eZl8GD7+s+LA6sH3FA03cirCzXNk5/5zVb2l3uY1K+Ak4brNzuL9o7BvLVKf2d/eahBNcJOpZ7S4D6ja1S6O510dzoC0fiK0udPwKMXQKXWlTEX8EHxNnhqBGzQ2+2VW0p6aiPln8PpldOraWOFoJ6Pr5U1awyOXCNfH64UU79m7bvw1hUw947WHZPNYUepp5SADNAmNczIl+5SBXc7voNFz5gLkRs+Vv83caEPVLimSTF5oZ679VBoIdfMb7bS/faP2VcW3xj//PE6ABxCkJqp3gftYKRCZn6GmjGsKgw1lk6HE7/mr1PJ0SEcjftbdaNeqxvMFIuRl1l65lLn0er//WvgqWFQvAW+eBA8FTD/fvNacczAMpMykchGZz2BagAPUHZ42Pij2cgnQ+UB9eM08lW3JbYCz+bIx5DKDYkXr5wNTw6ChzrCi6co5+CnV0OfmADZjKaEawIa9HYocbKuIlTkzDDaf/tsQ4Ou6XQIMjKzKJT5+CoiaxnzM1QhUkl1aBjUMODl3vLgvnB5Yodw0KjSGd0wG0Y+WUq0QecB8HjRcewbfgOc9Gd17vL/ms9zpSht/NXmukDMkI4FIw+/Um+F2BiMv3O4TKf77R/T/faPqfW1XhTh6DXy2Z1B86l8eqNKztaZtwnDUFEMUY5858rIE6vCjF4C9MedwolP83Hi7BPZVratQc8NaBrdk9YD0D1Qwfp9ysBavewdxdXsKq7mm00H6X77x/y4rRiAn3aWsHp3GSt2lYYspDqEIC89iQqZhr+mnHCyU1VYqLgq1MgbYaf3N78PwMvTXub5k54POUcIEVSRbBD6TfinFPX5fOsfxpIBt7Ouwzn8O3AqD1WfA13GqOJHI8MmJRsKf4yUNonDk89IUka+whcZrooXIwRXVGka9vOeW0RZdcsIuYVz9Br5DL2g45Wz1LQNlMFP0KKZzdGBUXEaLg8cgTtMMyVB4RpQrfYeX/J4PWeHEtDAo89QszUNt9OBL6Bxxv+ZvRR+3FbMhEe+4LJ/q961c9fs474P1nDOP77j9KcXctYz33Ko0qy4dToEOWluAjhI3zYX9q4ElKxx99s/5gf9JvGXT9eHGHqnQ8XkM5NUp6wR7UZEvJ8OGhmu8VbhBd7MUtf+q/dyzn9lA5ceuIRqUiiv9Sm9dqvn3XNScPM6cTtnex5QD+LQ5DG6fTXFkzf+TrfTrF9YtbuM0Q+1Tse6o9fIG4us+1fDO1eZ+xO0aGZzdBDVyEcrLvKEeXYJcBasr5niSmnQczUpOSRVJsyL/mkAVHnM0E/bzMib1iuLtvPSd9tD9m07ZMaenQ5Bm/RkBjn0c/Q1rEfnRIZ9Rvxpnvk84Qw29AjvpGUghGhkuKYar2UBM6Cpv6tIv8mkJ+uflbUjVuUB9f/g8/jeNZrdUl9vsTbUjoFbX8R+ec3LDR+rMUbdk6/2hQbls1ISl+raEI5eI28XQtnEgWHkk5x6GuLuZRAtTv5lWKeoBKhW9soxi/oammUT0CRCX3gtlllIKdlVbN54nrtsJJ/fNDHkOb6AMrKP/HwI549SaccXPG+2wnMIQc8Cy9pE1+MAeHOJtZ2EiRF+MFIoq3xVMbVlGr3w6q3Gb8Tj/S6G9OgW+jf59Wte8hbctB7uLoLxN0HnY2Haw+SlJVGK3ou3urjelzsmT+Xf76lqfN8j4+88VBn6PTpU6WHe2v3BauWW4ug18v3PgPx+BOXwR8xQsbuC/q06LJvDC8PIpzh1T3rV7NATpj5gbs+aYW4nQPxuQJsBwe2GSh0rQ2GMwUFAg1m6MT5rWEdGdM2ld9tMVt53EvN+bxr7x84byvmjuvDX6ZHVp93apJGW5ORG7+/iGoOxDuDTfKw4uIIqXxVp7rSo5zqEo1Ex+dKyUgyHuOzgGbx+1diQ496Afk0hIKsDOF3Q9yS4ch6k5zO4czY+XFSJNKguqvf1MpMy6ZXdK0TmoKEYsxqn08XIbrk8dZGp6HnVK0voFaXWoDk5eo28ELr8gf5DGHSuaqhrLcjwe6E2coHJ5n8HY+E16MmHt9DLaAd9dA2ate+Z+xPQRagg1Wyc8+WuLxskOxzQJA79uywRaFJSUatuFPeeMTB4XlaKmz7tMllxz0ksvG0yPx+pPHghBA+eMyjkmn3aZiCE4D1tPADaxjmc+vdvYo7hgue/p/vtH7OtbBvFtcUcqjkUs6pV0LhwTVV5CX7dUZPSEdEwxBeo+3MwFpZLZWZcRh6UobdmCjUUY1YmpZNubdI4c2ikrk9hScs1QD96jTzABssdM6O9Uqi0FkS9dQU8PTIhi2g2RyaVPrXAllKxX+VZb1kQ2kYvJSd6M44EGHkhBIsuWkTnDGV43970dj3PMFHaNaFGftHWIqYc05a89MgK2Ow0N51zQ73sCb3Nm0y3NmmM7BYa4nTsW8navcrY/f3CYcH9fzo79OYwLPNcAHZX7qZdWruo460vXOML+Ji9cXbEjMZZW8QTeUor/8YTVSild1szJFRfLYBPN/Kd2A+rZtV5rkFGUkZII/aGYvydVV6BiNpYD95ZtrvR128oR7eRt5LRVuXLG7FPTYP1H0HVAXj/mtYdm02r8cPeHwDIfvksePZ4OLRJhfUy9AX67M5mfvWg6eYTE9QPNCMpg9lnzK7/xDA0TSKE7hlLB5oGFbX+YDOReMjPNG8Gn94wIcRL/q9/CuUyDZDkprk5c2hH+rTNYEKffC4YFRrK+G6NeXOI1dSjvnDNmxve5IFFD/DG+jcAqPT4eXn5h6yo3MKnGepv6pmvbrbvXTOOG07sw29O6MXWQ1V4/LHXMwJ6EdsBqTdViWM2kZmU2WgjL6UMFoVpOHh7mRJ6++nuqSHnnTM8tgR1ojm6jfx1y8zt1NxQT37fCvPY6rdadlw2hw0Hqw/SIb0DOUZFq6cc2vaHS99SncbaDzI7JrWzeLAJbPqckZRBbnIuX+36isKK+tUfF28vZv76AwQ9eSnwBjSqvQEyG5DBkZbkYvX9J7PtL6eSlhSaUbRediFLVNOWUt753TiEEMy76QRe/dUYklwOslLM8zWP6b0H1zbCqC+7Znv5dgAeWfwI3+3+jitfXsxjK+7gluJPg+cMb6ti2xnJLn4/tS/ts5KREiprYxeUGYvNz/nPUDviKGJLcaY0upnLk8ue5NavbwXAj5PJ/dRsKTdsdtUlL/raRXNwdBv5Nr3g5o1KxEwI3ZPXf5w1paHnHmxkQwObI5oSTwn9csP0j7K7QPvBMOZq9XjKXXD+q3DMaZaTEpsh0Sa1DeuK13HKO6fUe+4X61WKoJFdIxEqXxzISGmYtnxGcmRj7Bd/MZrNUnmavRx7SEuKVFOcf/Ok4Lb0ZzHv3C+4YcQNXD7g8qiv49f8bCmN7B6lSY3BLw/mzQ1vBvc9uexJvt8aWsU7ts1UOmSEKoUa6ZNVnlBPfsO+Ck75+zfc+/5qarwB2melsE/qs439q6OOz0pjMoF+2PsDv5n3G15Ybfa4cGpuHjtvaB3PahmObiMPkNnOFDFzOExPPhCWzfD8pBYdls3hQUltCXmuMK8qPOTgSoYBZ+oL9zoJ9OSBOnVfwunWRo1XWGLyN7yuultlNtDIR2PyMW0ZOkzpwfQRhVGNfEFmMt//0dJkRcvgysFXBitGw1lbtJb91fuDC90Gc7bNCW6f3ftsAAorC+nWLjTWnpsU2a0qwzDyXtOT31lUzclPfs26veW8vGgHCzcfokteKiulnq768hlQvDXWnw40Tuf/sSWP8e2e0I5Smf70kPWRC0c3rUVjY4nLyAshpgkhNgghNgshIppgCiGeEEIs1/9tFEKURrtOovhgywfM3T634U+0xuSNOOvVX6n/M5rWZNimfmJ5c63FrA2zOFhzkJqiMDGuWIVJqTlwuSrdT3T/4LyUvLjPdeie9xXHq5xxiYNyPWTRJTcxYYDk3E6UyTT6isKIUI6B1YA9OrdunRyXUNcwFrpBpRpuK1dyDtP7TOeusXcxpcsUClILyEoJvdEOKwhrDAQkuZT5ev3HnUgpeWtpIRMf/SLivCvG9WA3BQT0MfDUcHj1XKgyZwufrNobzE4yGo8DbD9UxYMfr8XrryeLJ8pNwe1ODpklPTx9CHNunBARn29u6jXyQggn8AxwCjAAuEgIMcB6jpTy93pv12HA08A7zTFYgM+2f8adC+/klq9u4VDNofqfYMUakzcUKpMyYMTlkdokNgnnyaVPcvb7Z3Pzlzcjj06LAAAgAElEQVS39lAAeGnNSwD4wuOv7jqqT5P1wpoEe/IX9Lsg7nM9usFJTdINiDQNSXiGTGNpk5nCetmVwY5tOB3RM0SSXA7+PWMUQHCBMRb3j1NqkO9sMk3DS2te4rkVzwFw6+hbSXYmk5uSS1FtEQEZGmfvlB5ZSVupV/i+smgHA+6Zyy2zzXW2OTdOCG5PG9iejCQXTus1t8yHXWrRfVdxNb/7zzJufGM5ECoBPemxL/nXN9v4csOBOv++4trIQitncmrEvmPaZ0XE55ubeDz5Y4HNUsqtUkov8AZwVh3nXwS8nojBRWNv1d7g9uRZkynz1K8RHcTqyRudb5IzILOD0r44FCmvapM4jBTBz3Y0b5/3eDHy1O/ODE0JjOnJA8HiugQb+ZO6nxSsFq0vVGAYecP2Sv1nPL53ftC7bSq5aW6Wa72UxEEd/V6P75UPwKmD65YLGd9J5d7/uPfH4D7rbNxYsO2b25cyTxnpckfI811RmmKP6WHKQ9eEqTz2a5dJz/x0zhneCYdDmPIHVnTtnz9/vBaAZTvVomw0xcxNByqp8UbP4qn2VXOo5hAD2gzggeMfYP6kfzBv5248KQVRz29p4vlGdAKsdc2F+r4IhBDdgB7AghjHrxZCLBFCLDl4sHGe84yBM3j0hEeDj8e/MZ4NxXFKqqblqdX1skL4+hG1LzkLOuqyqFUNnBnYNIiJnVXlZWu02otGqaeUqZ0nkff9c6EHYqQBAmB0+0mwkU91pfLrIb8GTPnjWBgpgw5hxOQVw7rkJGw8pw3uwJRjh+FEg1pL9DVMGiA1yUm7rGQyk+vO6slLyWN0+9EhWStOYcb6jVZ57dLVusf6jBdCnh/NyLfPTmFgR7OG4Vw9LXFi3wKEECy4ZRJPXDBMv36U2cieZeD3MHeN0rQpCZNpALX2ACocNeVvX0b9215eq3Rukp3JnNPnHNq60mgfCBAIX+tpJeIx8tHmarECkhcCb0kZXYhDSvm8lHKUlHJUQUHj73LTuk/jhhE3BB///MOfx/dEw5g/YVYE4k41dW52LIyrSz0V+2H/2jhHa2NgtH9rdK/PBFPqKSV7g+5NWrWO6vLkg0Y+8fojhoqjNW4dDW/QkzeMvDKQV07okbCxCCHo012/nuH8LHoGHukBq0JTjl0OB744fjdJzqSQhdcqf2RjjlgOQKyQ0b8uH2WOwyn44pZJzLTssx6L4Ku/wmvTGd1dffadclR4xSmcSL2C+GCFeVPaW1ZLta+aPy36U0ge/T+Wqx7TN464UfWS3ajPVI+g9n+FgHVZuDMQS73nQpoxVGPlysFX0j+vgTo0+aHd4ynor1IrDRnZBX+GH5+PfF44Tw6GZ49r2Gs3N1oAtsUuQT8cMErFG9soI5FIKSn3lJNteJO/tISQWsGTB8hKVl7p1fOurvM8j18jyelgr0eFF4Z2yeG5S0eQk5bgWG+mnk30zGi1ULlTFzPb9WPIaW6nwB+o/6aX7EimNmBmzUQLtRoCYeHEMvJGIxNQ6xE98tOjhqycDkGFMzvyAtu/YfF29T5W1PrwBzSEEARkgEOVkT2i39v8HrM2zuL2b1T+yfay7cFjw9oOU71kv3pY7TiCGnkvBvoIIXoIIZJQhvyD8JOEEP2AXGBRYocYm8ldGthdPbd76OP2g9X/+X3NfXNuq/86jSyUaFaeGw8vnw5bv2rtkcSkQpfrbUr/zERR6avEL/3kJOdBj4mQZ/GCdY86Ks1o5Md1HAdQbwMRj08jyeXgLztUps/FY7swbVAzhMC6Hm9ub5kP6yJ+9gC4nA78cXjybqebzaWbWbRHmQhjsXLRRabJcAgHn5wTKeCVGiWNE9Ti77a/nMqiP07hgtFdY762Uwju6/qymU0XhfJaP73v/DToyZsicGZgwphtbSxRa3pG8se9x90b0bhbiqansyaCeo28lNIPXAvMBdYBs6SUa4QQDwghzrScehHwhmyUaHTjuHygWXgRV55x+J11mn7HjZVN8crZMP9PjRxdC7LmXTigh48q9tZ9bitiePKNbV6dSAwvMrt4G2R2VM2wb94Idx9SSoaxaEYjn+ZOY2CbgUEtmyALn4RDm6j1BfAHNHwBDbcl/BBorpum0wU3R1nvCpuJbT5QySer6hdX652jmoSHz1TCc+u7ZHXh5EMzuKzMFAlLdcf2ioUQdMiOzGSx4nQIKkRmxGx+QWBYxLmGJ+/1a6R0fpW0bv80r6PP/AwxOcPu9FnxNvw9rPApWl+CViCuoJGU8hMpZV8pZS8p5YP6vnuklB9YzrlPShmRQ9+cpLvT+dWgXwHw7PJn43vSb76Fc/8FN62D9DaRx414celO2PoFfPNY6wqYFW2BNy6BqjoU9DZZOs7EoZndWhhGvsU8+dpy2LM86qGSWjVFzw1oplHPbKeMfV2I+rNrFm8v5v4P1zR4uABritZQWFkYlKvFUwmf3wsvnsKQ+z7jltkr8GsaLqf5023WdzOzPZz1TOi+GDfp+vqYDso3s5hKa1Q8/ndDo8sauzU3Z1eYMfu6jHw8uJyCgCZZtNNc1F6tdadTqo9xrg20zzIdPadwIpF4/QHcmWtxpu3EkbQfR9J+bvsmdKZvZPulbpwX0XlKHklG/nAmO1nF2RbsiprQE0n7QTDkfMgKk/888//U/x117ec9P5nHPrjW3G65iYpi6UtKSK0uBb22lrWJuX8MVdo8TJBSBo383qq9DH55MEv2LWneF324Czx/QtQb5IFylaLXLuA3tWniob7FtN1L+fpft/Lit/X0bPXVwLu/ieg7bHRWqvbrxsirG7qqg3gDAeYt34IvIHFbYtR+mvnzHnIhjDMTHcI9+RtOVN5xaT09TK0FXxNmKV3495aVhPSZNRBS0sfn48LyCt4u3BszXBMvTiHwa5IPVqr3+0cG4sdJP+8a/uO6n0lZpiqkEXbxBMy/05G6k+R2H4dcc0vpFv70vZrptw1E+QyOoJj8YY2hlWH1EkB5iw3R52bEZer/HQuV5EG5JeyxarZp3Hd+H/nc5sTIRijdGfuc8IXMB/Jgn0Wjo6YEdkQulWhSa3hBWSOpDdRGLLjO2hCf9GujsN7ofFXq8/OaXtwLq18EoJ0/AMdfF/916wvX/GsKN7vf4nLnZ3Xrp69+G1a8Dp/fF7L7kv6XALB432K1w9Jr9ArnHNak/Ap31V6clnBNsy9kO12hzVPCnIg+7VS4paymbiM/oM0ATugcWrm69VA5Ww5GZhNJqSGAO4tKmFn9C1Ka6MnvK69lyfZi3E7BcbVPc3ntLfgwr3lBO4v0r15cVlprLgyndnwbV0aovtXZ758d3M7JjrIeIGwjnxCcDidDC4ayt3IvC3YuCOpRj3x1JFPfmlpvzrGVQ11PVRvle2DePaEHF89U/7f03dmoxK2ruUm0H/lz4+D5ycq4vXIWvDgtIuz0/ub3mTxrMn/85o8JHHB0NpVEFpqlhjfHTiQf3Whu15arsNtDHcBTSY2/hpWl6gebe8HrdWfThGOEa+qZLWVSU/ekzzDuYZ+dYbBv+EL3nC2e/tlOpY3iK92DTF5vPicOZcWEEva356SqrJ7S6shslHCObX9syGN/2QhqfVFumPpN9FzPfbzLFNzOppmq/eUeqrwBNCnZSxtqSWa0wzTaHTp15daTDaE69VqHauNrMpKbnAs5upEfdol5wPbkE0dBagHLDizjhi9u4PEljzNrwyz8eglzUW0RTyx9gtfX15/ZeddmPcvGUx6ZQTNHN4TNaZiiYTQlrmthOZbB2bNM5e3u1cu9K0IzX9cUqbjxR1s/auoo6+WST9SX35qB0CYlyppIolj2irn9w7Mqxxugcj+XfaJmbe38fkR6fsOuq4cH8cS46eoiZhmiBq0uK2/cvMMagp/W01S6rPRWwhcPBR8PdShhrSo/1KSbKZ+jBlwY7+gTQ1joMDtVrWOU1uPJA7gscWpv8XHIQDq1UfTgNT3u78PVIPnk+ti0P3oNglvzsadUfRard6vPtkoPlbkdSSGFW1lhoZmZJ8+EgB+6TwiRoy5JDltAbyWOCiOfn2r+UF9b91owTgbw9LKneWH1Czz0w0PRnhpCDbpHZ0zru08wp+dGxxrLNH3OtjlsLatb0a7JGEJqdS3+Gt5gTliTY2Dw+qd5MjeHg06HmqEYT5FaiLxrIvjvuv/ywZboaXYG751lttDbXbnbDEs0J/vXmp+pr4YNJSpj5ITqmsi1mfowiqZitZLTp/gZ1MQnRhymhpqdnM3DE1TW128//60KH4aheWtJCpgGJCsjejemhHOpRZLKcnPKSVNG+NevLg02945FsM0igFSG0+PTWLunnJnfbA2GuKTe1k9DUFxV/wyhPt67RqWn/rDNTEw4z3MPazX1m3FILxv2qRTfuWuUY7XlkApl3jb8YUa3Vc//bUkZHxXuJdOtUikndZlE39y+sPM7OLgea52o5mphhzAGR4WRL0iLXT0bq7FwOFJKqqVu5F84Sf1fWwpXzAk7UX35AsCtX9/KWe+dxeCXBwf/NbbZQEyMmHydnrwfHO6I2PKdBcpT/ndOFlO6doY3LsYT8PDE0id4b/N7Iefe+tWt3PvdvY0eZpmnjL/8+BfuXHhn1ONdMrtwWs/T6JHdg3k/nwfAJ9s+4Zdzf8kv5vyC0tpmFC71Vpozs1lm2u21JWUNN/IOBziTTYE7K1VFwZvyWc5v41ujb9MrYtepPVTYMDs5SttB4A+1TzHUvyPqsWalt0VaeO/K4GbnXNOY7aqnd+mkLpOC21I38i9+u43HPtvAnz9ex3NfbdWPmVr5iWBQx8j3crE8hku8aobu1Lw8H6yUVa/59nI1lvSkNDrqaa3HeL3kahqX6WsnfXIsKZlVB4PPLSUDR4wCrpbmqDDyVk8+nD2Vpve6r2ofV869MmqxSbU3wEYZOr2a454KXceEnqh/+Q45o8fbRr02it2VCezfaKzw1+XJL3zcnGkADL0IeclbwbZpQWrL+HTrp7yw+oUIgz5n+5wQhcCGEowhx8Dj9wRFqNqnt6dXtmnclu5fyitrX4n11MZhGMh+p6k0RB1fsZI6PsbjJfe6n6I9s36cSaYHblnMZa+ZrpklatDqKhBqoxuHtpFV20IIClILyLeEs2YOeo23A0pZsZdjL/laK+ksnf+q+v9jU0nUKqf73FdbuOu9VTGlefNT8+mepbKZhnZWf9/89QdYoDdC+euc9Zzy928or1HOTaKMvCtGTN+LmoU4Al7y0pNUWz6pn+tQN/J0dwqX9f8lVxd5mFCtnK0sp3IIe+f0Br9lpqG/F3MYj1PYRj5hGEa+X24/Xjv1tZBje6pMIz/1ran8sO8Hnv7p6Yhr+DVJGWZRxrP+M/jNplHc+e4q8yQpg7Oxva7Yiyrri9fHPNZgDE8+1gJyIMqiqzuVDx3RPf9HlzwadX88+DV/sNIvnKX7l9b53JpADclOc4EzXL9mZ0Ud2UONwZUMI6+A3G4haxFlutDVuRWVkRXQ8eJ0Q00xfHCdWsy9LxvevBReOzf0vLoW/Y2bcoz1lIM1B3l787sAzE07gz8vcXCz77fB4x5Hy8rVBumnJyfsXxX18Ecr9/La9zvpe9ennPl/Cymq9HDbWytDwjjbdQ35tlkiaq/TdXvLg6ZdS5CRj8aYHnlBI+/U1O9M9chV3xHhVL+hNt5i8lNzua58P8bqwIVlZTw1+SlO6XEKlOhO4+irgn0p/DhiSjG0NEeFkTckYwcXDGZI/hDyUvLolNGJfrn9Qjx5A0PS1YqmlzCv15RMz9faEAD+88NOdvTQtb4r99fpyV87TOXTv7ImgV6pYeQ9MRoL+8yCkT2ZBQzu0ZXvMnOjhk1mdGgbzFU3GNthbNxDuX/R/Uz/YHpU1U8jB9rtcFPlixSe8vg9IU2ew8Notf4EFpz5vWrq7HSrfgEW3sxSsdTc4+ueedRJTbFKf7Qu7q77MLi5MKAE8KSnDqExY22nnvRHj4DlZZGCbj6RuMXIBuF0me/pelN+IJqO/crCMh6ft5E3l+zi3wvNtaux2SpkduvY3/LEBcOiGnoHRkzewXVTeifyLwDgw2vH8/Ivjw2mUQrNC9XFnOD9OphCmaLnxRfMuoD04nUhz3fOf4DJfoeaxSz/j9rZZyoMOBum3M0/5HkcJo780WHkj8k7hltG3cIvB/0SIQRfXfAVc6bPYVjbYcGUSivRVBA9AS8Z/e7hF5njqBlyOZ5Opm7Hzgy9XNlbFfxx7o/iyU/vOx2AZQeWRRxrNEZYoGR7dIVMr2lQvxbKUP56++yol1qWEirf8OjER4Px33hYV6S+6D//8OcR4lI+fZw+zcfY/44NSV2t9dfi1bwheePG85McSXTO6JzYtYy5d6j/i7dCeuh6zYd6COuE0Q3IjW8gH2r6d+dAHFWv9VT/zklPj+rNtponD3CxvmD/xkVQotYGXpgxOuqp//lBzdACUrJ0RzFbD1bSyXEqbH2M7rlqwfjh6YM5bXAHfrjDjPnffrLKdNMQnDm0gesm9dA1L43BnbNJdjkAQa104wh44b3fMuSHm2hL6PpQtqbhLtlETWZ3PguMNA+8cqb6TRp9KLoep9ImJ95CqUyzwzWJRAjBjIEz6JIZ2kMxluHIjCJAVeGtRDh8VLX9jk3H/ollu8oYqutz7y43ptZ+jHjNhqQkXA4XFx9zMcnOZN7vdBZtNPWhGivvCSGY1ROIPv03YsKn/S3i0NfHP8Zbu/fyh4rQ7IScZPV3dcmK7Dm5/MByvtvzXdSh9Mg2K0PHvzE+5FhNoIZUSzbBvmozv9tobjxnu7mIvU73jC7pfwmdMjpF9P5sEmv1ReWkDBj5CxViGPkLQPVFPb3n6SFjTST/mvITXwXULFCU1rE4atzvlr5s7lv9NqwJXRCvEYKA/jO9YFQXvs88iUKZT4VHfS9crVE6b10Qfk+FkLLT3Nw2LbqCJMC+Mg/Tn13EL19aTLXXT1qy6SQlu5w8c8kI2mWlcP2U3vTMT6drnvn5dMlLrC777N8oBVljLcGDG4e/Gjaq7+f1rtDPIE1K+PF53Pgok2EOYuV+2PAJ9JoCKeb7EtCkHa5pCWL9kA0jZ+WznebUc9YS1SNlxS51R/9yUwnlDkG1tzLoeW1xu+mU0Yk/jvkjS074Bz0XPo14/xqm95lOSp2dhRpI1UFT6CiakTfCHGEe6/l9zyc3JZd+Xh/nes0vW6ozhbZpKm6Ym5zLxM4TmdrN7Dl52aeX8et5v46qL2PV0IZQ792v+UMWwD169slLq1/i2RVKV2hUO1Pn+/y+5wMqlTPJmZRYT96Y3XQdC64kuOj1YJGKNyU7NI2vMQwwKx057lqzAObSt/EGNKpIDR1HVHQrf2AN1Oie41u/hNkzYOUs3pn4dwD8QiARnDu8Ew+eM4jUlGScaGgyQJqm8dNljVw8bgrWfsg7zObVdTWqNtoDbi+qptobID1G39ibTurHglsmBSvMNRy6x9100nVpBCPl02CT7IzjgFkhnqTLRAgpOKVS/wx3/YCrYjcewsJkhXoKcJg0hialnV3TElwz7Jqo+2WUDOZ/rnoyuF1eo+Kkx/ZQcWY/TsZ168KpX98QNPIrU5LZoeufBMuXN35KdnI2JZ6Sukva42WfvrhlxG2t0gbVxUqqwDDyrtRgdx2Afnn9guNKT83nT13P5P/2HeDTyc/ytxP+xvXDr6dDegfapLbh8UmPc9eYu0JeOlrPymUHloVULI54bQRSyqBB75VjZswYRtvomgNw08ibgttGY4wPt35IsjM5sUa+uz7LONaidtjlWLhlM353Cm5HE+PZhohZSg6c/CCc/Q/4/Rro/TOSXQ5q0W8idWVEWash/9oNvnncfPzOVXR6/VIAvAICOBjVPQ+X04HL5cZFALNVSCuQaWn1ZykSykyJbrjdYQ07Nh+orF+LRpp58iJBYY8/nzOIi8d0JTks1LpR64zjkJlQUC3VTVoKiSvsZ+whiRM8ls9qli6HMvi8kPMCmrTDNS2BIV4G8NB4sxgqmpea4jS9/iqv8lD/PWMUv57YE6GrFBZ5y0IEylIdSSo9z+Jh5yRl49f8XL/g+qb/AXtXhD7eYQmjPN5fSRWU6Q2UXcnM3zk/eDgrOUtp1gBktOXs/OGcUFNLm6RMumd356ohVyGEYPqz33H609/QKTN08WvyrMkRIZQafw21/lqenGzeED/Z9kmwEcSItiOC+w2jba0UtC62HqhWKXPFtcURHYOazKbPoMvYyLLyjAK8AW/Tjbzx/CTL1D1bpd/uKq7Gh5OAFOYNOCphBmD+/SEPk/TZm08INESws5Hb7caNnzS3RLSwVl4IPfVeDpZZq8vp4K7TIlNCTbkAxfp9FaTFaeT/Mn1I08Zp4ZzhnXnonMER+/fLXPVb0YvKhMUJdCHhNjPs5sHNDtk+VL4AICmN0movQ+//jCXbi9Ektiff0ljbikUz8n1zBgS3F2xeB0hS3U5Sk5zUBiwfltQwlnJ/WXQA5tweoliZpnsEXxZ+2XRJ3XDDN+9uc9swILNnALCkciff7janzl0yukD3cTDgLDj9cdPgWVL2Fm8vZumOElbvLo+acRSeLikQjO04lhO7mgtkT//0NDV6IVObpGxemvYSYBr5oJoihKRQDi5QP7YnJz2ZWE/eUJzcFV1Izhvw4q5PTrg+DGnitLyIQy8v2gEIqkhFVNah7R/wQV7PmIddteU4AC8CDQdJep63251Ejqiiu7a99Tx5gEtmw5jfRMh/TOgTWZiYFUWWIC1GuCaI/ts5vlfzN8NOSdOdDz28loWZfnwgqx2k5kCWcoJ6d1Cf+aFOU0IvktuDH7cVU1bj45kvNgPYnnxL8fSUp3n2Z8+GhGiiqfatKDJlbzN6P0ZS/jxcTgdpSU5CTK3UuKGd+uKlaVIJSFmqH2stmiY7y5uY+x1nj8gih4Mrfnok+PiB4x9gYP5ApbNz/isqH9zwqC1a4N9sMgtqoq1fuB1uqn3VepecABIZXOhL0rM7dlfuZtlP/wYgZfOC4M3CMNqD803PybpIeO2wa3l80uNM6ToFh3Cwv3q/0mppKsb7Py4yRVJKiU/zBcfeaA7odRD7oueKAyzW+uHcG13LHm8VlBdCjxMij538kMrvR5Kkabonb8al0/UFywCt/ON1upXEg+aHJS8Gb67hoRmAbm0is9nq9eSN32sz90n97vYpXDFRn2no3z+vxTh/K/WYfHs1o0hPV9/vjUWmVfB3OR5SsvDoBWCGmNph4sgf/UZ+UpdJjO80PiReHO5hV9RGplkm5Slp3r1ltQScFjMvNb5JUwZxn8sJBf2U/IFuwEY7zBX2nw78FBQBaxQperjJ2rTBWxWhd/L7dqEVv+f0OSfyWlE8+afmm8qQ0bzb4tpixvx3DENeGcJZ75+lztNDFUsvWxr0zO/apQTO/OveDy461/prCWiBYKbOnOmh8hBJziSmdpsa7MID8K5e/NMkjBtFp8hmzn7pRyKbHq7pPi7qbmvT530yD4chQmZl/cfwkJ4SmNMVLnwdplq6jxVvUxkbgFsqgxPAQQe9yXTbFD1WLUTrevJgaiV9dKNSOoWoapE5aW7+c+UYPrzWzMjaerCuRWnM1NJmNvIdc1JJ8Vh0iNoOYLgnyqxS/4726qxCOk5LzcdTWzvy9tJCDuifvyGoZodrWpi8lDyWX6Y8q6d+eopVB5UXtmR7MYPv/zjifOGsQUrJku0lbHBYsnE2zQtu1gqhHpdsVy3kUrIZ4PXy/tmq9+Y9393DhR81QSHQ+KJ3Hg2T9eKmhzrCvpUhp7W3qPgtuyxGjn4UT96KK0o/yl0Vu4LbxiKz1UB+cf4XIedXoAUNvzfgpcpv/pA7ZUQWvBjcMUbltT+y+JGY58SNMauKkuFkZAM1Obumg1430XZgyO5N+83sowrSEN4oSpUbLP1Ls7vAMafCuOvN3qMDzoIqNcNyI/EKtfjYMUf/e3RJ21b35MHskQzBClhXFE8+oEnG9c5ncOfsYAZOtGbbIbSQkQeConIAHHMaqZYmJv/M02/ougyFO1l58t9uNz/rpwNnc/PsFfzpI9WC08jeKaxHx6eliOsdFEJME0JsEEJsFkJEbfEnhDhfCLFWCLFGCPHfxA4zMVizT97e9DYAq3eXgdBTActDF2WGvDKEiSO3ILuaf47/h2fp71Ge/SlV1XBog+rcVLZTyYzuXhI1RbNRaJYvulUS15qJAfTzmuGnmF5q0JM3ZzHWPF5NM78K/zdFdcmyqnkGnyOcqqJ0zbukOkMN6ejaWpL1UEhtoJYdZfGJaFlDRU3OSqrDOBiFcU325DP19Z1jQgvJDH2Ukwa0I4CI0UVMqPz9a36EQRYZhI7D4L4y6DFBhdiAJCnxCoHD4SQ/Xfccj1cL+hJwtubCK4T2MNVj1i6H+b4bLfXy0s2bqi+gBn3Z2FDF1AiCs+0W8Ian/dXczutJqqXZd8fuekht8h9h/E2kDzkdgK+3mDcGGWZGVxWqY4u3t7DOfwzqNfJCCCfwDHAKMAC4SAgxIOycPsAfgXFSyoHAjREXOkww0vj65Ko787q9FQiHMpKB6siFsFc2PYZwmXfke/PzyNEC9PJ6GV0bNq3rMxX2riCrJgGxZQg1WMMvM/eXWwTQ8vsSOFGlP0ZbPA1eSjd60rIeMbSzmX20do/pdddVYDN3+1z46q8w+xe41pmywgM9Hnr6/CTrGUHegJc7FioP/ekpkVpB4dwy6hbATK1sNIZhjWIb1hxSoTOv1sRMnq5jYcaHcEKov+PRZ1TpyS40HJGzpoBf1T2kF6gwX6ymElnqJpIkJT4hyEpLMaf+epggIERIFkirYP2e9FG1FkmWcM2dp/Xnmz9MpmOOeRPvka8WOTvk1FNLIlsmJg+oWoqBeojTmUSWpd4jN1u/GSVnws/uJSVb1Qh4if0bWbZTGfc/hGUVtRbxvIPHAu2aDccAACAASURBVJullFullF7gDeCssHOuAp6RUpYASCkPJHaYieOCfkqH5uEfH6a0tpQ3l+wIevJSiz6N91eacqIfZGawKDVVvXHHnG6edN5L0EmVPLtKQjXmfYHImH9cWI28023KHhuhiN4/gxkfBZs+h8e9rXy7VX3xLnjuWyY/9iWzFu9i2c5S8jOU0Vi+0wwt1FXMdfnAy6FIZQ/w1i8B6Ovx8p89Ko6crHvltYHa4HXGdxofeaEwjNlP0yWHDcMXaeX/s15pjAxsMzDiWIPpMdHMstGp8arPIcXtVPnd4dlV7/1GVVXGI3897a+kaJIaIcjOiczi0aD1Y/LWm5T+HUx2myZlX1ltRLXq1RN78d8rxzC+dz3NWloyXAOWcKaGcCXTU0+jzsruHvV0oyjKL6OvQQBN7kubKOJ5BzsBuyyPC/V9VvoCfYUQ3wohvhdCTEvUABONNVd7wpsTSOk4CyF071Zzc03fZ+hQaRYGuR1ucEQaaVduD+gwTD0YeYXyBIyGEmGt+sI7vMeN4QkaX/RuqhybnXq/1rG/g8x2+KUfh3CE1AWEs3qv8tTTRS3bDlXxh7dVXH9Mjzy65qXx/NdmJtDwtsODXZtuGnkT/zjxH8FjXTO7Kq9G59P+1/Dq3v04p6j0TqdUGTjegBeBYGLniXGV3uemqPeuKM6WazGpwwP0BXwMzh/MmA5jIo4lgu1F6j3unJuKZvz4rSGbVbqmUJdjqZfOo8nRNMqcDjKzI418AHC0dFP5cKyfq26Urb1YJ/SNNORJLgfH986vv8CpJT15UDdtUGGn1Fze372XVdt2xuwctk124EX/yVzmC22dWZCZTHmtsidHUgpltJGGf7tcQB9gEnARMFMIERGYFkJcLYRYIoRYcvBglMyDFsKaQufOXk5KR/Xjk9LFxcOPY87vzOo1n+bD4aqgayDUy3c4k81iGCPf2biB+Gp4esrTjOukFm3m7ZjH6+tf568//pUGYXgzsab1+usFtEBI0VE4f3xnJf9cp8b/YlKo1HCy26HSS/UGDiPbjcQhHHx5wZesmrGKKwZdwYTOE1h44ULuGHOH6oJjZOIkZdK54oDS9jDeA81PijOFWn8tNf4a0lzx6Y4YdQxPLH0irvNjEvQAI7+2DRlPY9hf7iEtyUmb9CRTVMzqzRtrD8Yiel1IjdxAgGKHk/K2kTcFTQicrW7kIz15K23SG9A7N5w6PsdmYeQMtU7SfZx6zT9sg198okI5UdBwcL9/Bou00FnhMe0zg1r6R5J2TSFgFaXoDITr9xYC70spfVLKbcAGlNEPQUr5vJRylJRyVEFB8xc5xMJasQngTNWrRjU3WSluHMLBqhmr+MPoPwDgSCqiX20pbxfu5Rh90XVL1R4YfaXqYj/mN+r5hpF/92ombfmBAXnm0sVDPzzEa+tCte7rRQvz5AGm/9vcTtKNvAzU6S2//uMuSjBTO7Mw494pbielVT6QbjrX3BJcdA0nOzmbi465SHlgevYH3gr4RhdGM2Yxmi+oRVPtr45bCKxjhkorXHZgWYQccsOIHa4p85ZFVSBNFAcrPBRkJuPQc9vVcCxGPrMdDD4fMuL47uf3IUfTKHE6yE4PMzTHX394ZNeEePKRRt4aumk4hiffgoaywBJDT8uLmSobzsr7TmJI52xumto3RJPnSDLyi4E+QogeQogk4EIgvJHne8BkACFEPip808zNTxtPrBhxz/zQyceF/cz0R7eU9PX5mKh3hqkN1Kq7/LgbzLu9VSTsy4cIRCm6iloFu+INlR8dTtCbsXhM2Zb7bZYqpfdr/jo9eSPLIXChkojtLfZwnvNLtqdcTLasZOoAlftbkNSfjKTYi7dBqqJ0JTKeF/BTXFvM7I2zqfHXxG3krca3uCZSNyduZHTjUO2rZkf5Dvrm9W38teuhsKRavdfC0tHI+nn7auNvBJ+awwfen1HmcJLiDjMWHYbq2TWt7clbjHyU73qThMVaOibfAHL1mHufthk8ecEwslLcfHDteK4/sQ/pyUegkZdS+oFrgbnAOmCWlHKNEOIBIcSZ+mlzgSIhxFrgC+BWKWUTg6vNhxACZ/XwiP3/uCj0zu12uhlWoOLuJXrWQEW41KiVsIW4gBE7txDSHKNst6qefPfXQXkCQBmqV86GXT/qA7Z8TB0t405XcfOADISkh4bTJiOJE49pizNbecttRSmPup8HYNTBd7jztP44HUJvnBIH1WFG/sR7zL/doqFe4a1okKSvQ/87D9Y0JZQXPZa7p3IPmtTomR1bSqApFFd5WbazlKFdchAQPVzjq4nfyAMl/vZqQuIIKxxyuA6P7Brre2wJ17z92+O5Ylz3kEybBnMYG/kPrh3P85eNZN5NJ3B2WMOTdIuEsjWdtDWJS4xaSvkJ8EnYvnss2xK4Sf93RNApZQA7MTVn/jn1n8G0Siu/HfZbfj3v15TrH9hrzhE4WckxuQMizg3nqgO7eTnsN13trzYXf5+wXOOgpdvSju9gq6XQyPpFdyXBrVvM8n3qj8kHxZJ0idgxDrPLzYl7n4eMRzm+VxsqPXV3KQKUoSreqlqdpeaokFVme9inS7V+/xwUmOGFhhj51097nQs+uoBSTxMybGLkV7++/nXA7CKWaL7fqnyaYV1y8AW06EbeXxO1SCsW0q++J1mZZawvXs8xebpeuzNJZde0dp58ag7M+Aje/13I3zmyW27UTlERSKnSgbM7RznWgnnyDaRLXlpMjXurJ3+Y2PjWD+u1Fpm+E6jcdEfw8fEdj496npFlUqtP/42v3uX9r4x+4cvM0vzs2siWfTV+XfwoXIbW6uGvmhV6LPzbkp4fIm4VkPUYeU0qHY00lSlwhWtu8JjU00DdTgf+QBxWo3Snmpp3ORam3GXKzhpZCJX7Qk5viJE3mq0E36PGECNc8/nOz4HQxieJZG+Z+vyO69mGzBSXGZM3PFwtoATn4vTkpZTIgAqB3frd1Zz34XksP6Aqtj8pXs23aamUN8VTThQ9Jij5jXraGEZl8Ux4YiDsjyL90dLZNQki40gM1xytePwa0p9F7b7TGZpydczz2qWpePUUPRbv2X8G3pIxjIiS8QCoDjEX6AusmR2457h7Qg4H2+LF6tkKsPSl0Mf1fNH9mr/OcE1A6l1qnC6kdeGx4JhgKpvLIfAF4lDNNJQxwz1SXaY1nNQGhCeMc2t8TTDyMRZe++T0oXdOb9qktmnCtWPz/dYikpwOctLcZKe6gz1Kg5+lMfOyhDU0TVLtjW4cpQTNF+oNGzITr+37GoAd7lbq8xpOcnaoNEC8GBIhq2ZHtrY8jMM1dWEVXrMa/NbkyHoHE0itT32JfCXj6ZY0KeZ5OSk5VG68m90Hfo6/7SBkIBPPvnNwizrSw/qfAdldIasj5/U9j5WXr+TP4/4MwMfbPubrwq9ZsPsbBvfoyn5rQ/BqfcExvOy+Hm84Pk9eGT2RZJlmJmUE5VXdTkecRl6vGQgXNBMCBk2POL0hnrxxrlWeuMHE8AD3Ve+jT05kOC4RPPfVFuat3Y83oCGEoHfbTNoJPeQ07+6gDAQAZcpQL9lezOgHP2fAPXODlbIhfwYgfXkkCfPzMtRTU3R9oH6eBGrwN4XszircWL4X7suG/zs2hqRDGEZ/hIVPwH/CvjtHqJF3WGaQeeFZUa3EkfUOJhCPz/xh1ddDUgbSeTNwIoXnfxbcF6jvS5yUFvTahBAMLVCiVi+ufpFr5l/DDd/fC8BtBRbPsny3+nGEe78xcnWDY9HqTqEMevJgpnmmt1Va4FsWqJdwCvzxLLwa0/Jo+i9RMnMaYuRTdC2cRIVrSmtLmbN9DlJKdpTvqLNYrCk8/On6kMdZKS7cWDz0+fcrQwaqXSDw8+cWUVSljHRhSeTfa2j4ZLjMVnuGSJxfP+Zs7YVXgza9oaYYvtYF5g5tCCppxqS2XKXgGmwJFbuLFXY73LEKtKW6j5yK16OKj1fu5auNB9l6qIoRXXN44KyB/Gp83XHac/QV9NIas/I1UJ9BFI6QxahuWdEFmZamWsIe+1bDrh/U1L7zaLUvvW3U51nxy7pTKENakRnhovE3mnro3iq2HapiR1F1/QJhRrgmWuMNvRL27UKzWUZDjLwRcvp4a6QqaPyY4ZoJb07g1q9uZcgrSgu8aVk79fPDHaqZihACl9XI7/lJdaoCaD8o4j3eVRw5czG+XrWapT9BhapKbpuiKmCvKWlEiKQ5MBpYL3nB3GdNJIjG5/eFPs4Pm2UdoZ68VWo5UW0Lm8qR9Q42Ea9f45r/LmPGCyo1cdnOUi4/rntUDWwrRh55abU5PQ4PIUYgnCFGXgjBuX3OreMJKG2Tbd+o7aF6jn636AvCVgJa3SmUUlq+cIbGeccR5uLtzKms1JXziqvqCQHECtdAUAK5r8/HqBq1ENkY73lnxc4m6P0o6+iPUo9wZq8zI/Y1lXV7TSPcLsu8YQ/raFn70ALqu9CmN0BEFpPRbMKK0eSmOmDWDBh9d1NdqbT3+5lYU1d7wRYk+f/bO+/4KMr88b+f3Wx6AoSEGiD03qQIgoAcICpi+55iL2c5Tw/PdnI/Pc96cmc5vp7enXp66lcFTz27CDbEhpSjhd4CBJASSgik7e7z+2Nmdmd2Z0uSTXaTPO/XK6/szjwz89nZ2c985vN8SnbwskhKfvmL1veHNgdkzTbOiVejacqUfvZzVPGgcZ3BOhI4yfWXSwZHtZ0xmXLMZMm7I2l5h8mSP7wDju72uSPMiEDLef9arWa4MZEZRe9Tj/TY1oP3rfdKgu5j7QfDNbrFfGCd76I8WWVfb96/M/0c2LlrjFo+wFWlx5ncZoRWBqEGXN5X6515rKq2Vqp2PndXWK32KV2mMLHzRLsN6sQR/aYY2Md05xGTAnaXg7falzy0YJ3VlWE3FxJ4WQzJG+JzY1UISPVKX9nhuJNqo+QrI3x/du7FDR/AX4dr+SMNXdYgRrTL1p5ce7XNijCy4WhmSt6qwC4YahOfa4MxS37bPH87N28kt4Zw+C2TZ0fCnAGkHtgYNKy9MenWbYL2f/370KYfdD5Ni2A57dcR5TtScSRsur7FJ3/lu3DJ69qcQXYHrSBTh6GcN0RzSZ0IEe3hY7Ne6TLLxlKZ9AB00bKJzzhZzlN9rq1x7fZR7TW3xtajW2u0nQ9dOby/71vL4kv7XFq7/UWgSlfQo7pZo3bSxs/kQ88oitueoUWeeD0+xba2WJuUffFqrXtVNBPeqw6uYn3JekqrSilxnyC1dQ8Y/9tYfpTak2Kj0I5H8Ml38Dd9Ry9ux1vXQMkWLX/EU23N9G4kjO7empevHcFtk+pnkr82NFol/93WQ76GuUt3HI7qh2Juz5aVGn14U4ZNKFTEwwmnv56Hbo0792hdm0bmDeWl0Y9wUWkZe11JcO9+mDrbv22HoVo26337o3LXHCo/5Kv9Yoc5uobuE6GvqURy6R7Yu5K2J7Qb0IlICVGGu8dcXsHA4YRrTf50b81dLkahslr3e9Vvvn2ytDmQ189+nbVXr2V4u+B2gLHAaIIRmN055JTR/Lp6Jluq22idwzZ+BA4n1R4vWw+WkZWSRJ/2mgV8+5ur+eX/rbBsbxgRl3V8lnemv8O4fK1K4qbDm/jpxE+0b9nNXrnGAzt3TaQnUG81dBkDd22BwTY34IpjWrJVI2RC7zYRXcANSeJIUkNum7eSxxdsYsXOw1z83A/M+XxzxG0MJf/I+QP44k6bJsohyLDpLB/1xKvJ4q/QC2+NLS1hROsBbNf3+86Oj6FNX/+2RuehKKnwVPja7gVyotJNyYkqi7/YjuELzuca56ecqIzgrjmwHnqdFf4x2nAD2VQmjITxOWofYWP4srXvOjctQt3yOmIYF4Ht7LL1Pp+f7jcpwH2reX7xdr7bWsKp3Vpbml5/uu4nKkwRX8Zlk+PqSK9WvTi327kA/PrLX+P2uslKThAFD/bumsCCZbuXwVFTxXKPW0uiymyjPVGaadMPyo/4i94p6kSjU/Juj5eVu45wqEyzFOZ8rjWjfvarbRG3NcIeh3RqSZus6NPLzfUojOJEEd0aDqem5L729y3N9WgXfmeSQXrpVK3t48nlT1q3tUl9X7R7EQNfGciSfUvYW2YtAlrhrgjZ6GO17hro38Hmhwjwe3+JoQdcr4ZMzvHhqbb/UZsxSjDXIgvS+ByVHptmytGgf8f7K48iEOSkBtdijyVGoxBXQG9Th0OQ6nJQkGtVxv/6rgiAWyf2ICXJ6o5YtMnfa8cXI6Tv1qjMeaL6BJWeyrq3MIwl5sn167WQXMukgpTw4iR4bpx/mWmOIshgOFmihWQqJR8TGp2Sv/Ot1Vzwt+997wv3RD9BZ1jfds2Gw2F21/z7Jq1xx96jESxN4dQubsOH7UzmymPH+d/9BzmjVT+QXrL1yVtPoNWT2yNod7/+UvPN37DwBs5850zLukpPpe2kLsCBUk1ZFuSG8Nk7kyDfn71bHam0gfRG9pUaP97aKHlnHZR80XfwpjZxW1p9gkxXZtguV7HAaBTSIi1Y6Q7o0IL/po+2LDtUpn2uIZ1a0iLNxRs3nMqE3lo9nV++5m/CboRZGm42c6OTwxWHo2rE0mCY3Ub5w6BlF83AKdcTwowkP3N1UU+1NUJrmqn8d9l+2L4oZBa1omY0OiV/1gCrK+PISc3va7TcCoeh5GvascVcMrVjK232fE8kJe+t1kIK9+o/3PP+hgutPIKjRT5Ir69Uwun5p1u31dsIGhQeKgza/dqDWox7tbcaj/QEuWuOnKjiyIkq38Rg2IqAkx/yvfR4Jexa4o+hD/pcnsiVl+qg5FP0HqaWap3R8o3/iahSr2tfn1R7vPz1S21eqHVmsLts40/H+WxHNdwfuqHzad1zee5K//f93kqtf2+gN7BLdhdGtvPfjBNKyQcm6zmc2hzEn7rA4id8obUWy9xTbY3QGn6t5akSgNz6KwvdnGh0Sr4g1z47NZriWsZkVk0LB5mTGtJcTpwOQVlFBAVmJDUZmAqK4akC6WWgnpbuqy7YbqBtaNn9398ftOyyTy4D/MrQbLGeqHQz9OHPGPrwZ9z3rnaDCFvbu8toyjufwVZvBy3r9aUz4R8h+rJKT/SWfC1i3Y2bVYWnFkreVPOm0lsdcp4iFhw5UUXPe+eHHWPEw1d5gSve4e6MP9qOM7ttfvPmKq2zkC/h03/tXdTTn/ofLmQ27ggHGBPnO7/zZ79mmXzv7gpwBTxlBZTqpp5v0s2FRqfkW6YFf/HjeuX5LNZwGDeCulSHE0KQkeyMHIViZugV2mPsz1/W3i/7J/y0liQjcceweK//Eu7ZGbT5liNbQu7acGuY3TWj/viF73VViInBQJKO76aHYy8uc1ZoYKVM0C35SEpeX/+fG8KPs9tUT375fq/mkhv/5ngGvjLQf47C0cqfVVwl3fVqyb+2xP89Dexon/B17mBNqf1t0VboMYnVSQMAuGJU56CxL13jj/45crLKlwxlvlQdpieocMlvccecwNQi39/z+MA6rY4PgLsyYk0mRtb8+lEE0/iUvMktc+WoLvRok8mQ/BZUe7wRU/I9AX7O2pKV6uKVH3by7RabDkl2dNbDIPudr/0/ugvevQnjZ+r2ujlWeUx77E2x1n+J9JkMS95wcwAct7kBJUUI6RJ6uGPLw6v9C8017X0C1cCSrwNrDq5hXck6X5bnvwr/FXkj03ErPfVryZsvoW559vMdV4/WbjrGV3ii0sOFp3TkkfMHBo2d2KctZ/bXfNA3v7aC91dpk+vmK9VsvSeUuwbgsn/DL7Ryzhz1N4XHXWlNjFr1ur68ApLCfD/ZHf3lqxV1otEp+VSXk7um9OKh8/rz8PkD+Oz2cbicDqSMHNZY24nXQAx//BUv/hh6kHkiyYhGEQK6jvf53AWQhIPn1jzH2HljWXNwTdBuqryh440r3BUcKtduNHYTr4bSAMhIDq+YT0zWGnxLcybv5w8Ep156vZEt+Tr2UZ3QaQIAMz7yt198euXTkTc0uWuq6tldYzw43jSuGw+c2992zLAurUhOcvhCI09WuW3DcQ1mjNQs/P/uOsofPtBqrJvdNQ6ThZxwSr7XmdBJr7dknk/ZstBvyYPmq/d6teJ4dpPiebrr8tZl9SdrM6PRKXmAWyf25KrRBYD2I3DprohIkSG1nXgNZGwPv4UR0tLubkqhTzU9zpfugT3+xJds0+ST0RTCzJsb3wwpx4jXR3Dl/CsBbBXatEF+H2jEYkl6bH5SpWmS8OBG2LfaOi4aSz6jbjXbHxv7WNCyHi2DI46CMPvk3eWWp5tY49FvhrPO6kOrECVlhRDkZiT7wn1PVHlITwl97ozYeus+/K/Nij2hQijD4UqH7/UbdOuemmVvRE7ZfT/XzodL3/SH4SrqTFRKXggxVQixSQixVQgxy2b9NUKIg0KIVfpfiLZJ9YMxoTq/cB8vLN4eslepT8nXwif/ynUjfbVu/nXtCF9ctF1xKcCq2FNNmXutrBUvc0wWuFsGu1leLHwxaJnt4XSrSEpJcpKDm8Z1Y9qg9jx24UA2PDQ14vbOJE2BjN3wkHVF+RHtz2gKEU10TR0JbCbes1XPoNwAW/QKm6UOwZrSHfXqkzdKRUS6ebbOTOHwiUrcHi9Vbm9YSz7bJgs7pCWfyBOvZk6awiazO2hBB4alb2fJp+dA78jXqyJ6Iv5ahRBO4FngLKAfcKkQwq7B6ZtSyiH63z9jLGdYjFj5O/69mkc/2cBbK3bbjquLkh/fK89X68bldPD7adopOB4qysac6m0OBRs8wzIsNcvfCDjQ5fL6htd9Pmkzb04Ltu4NJX+yykOV20vL9GSEEFw6sjNpEVw1AM5Axd1Sn8QsfBv+VACzO0PVyegseYAekyKPiZItR7Zw0n1Sm7cIh7sS8kdyx4jzqfJW4ajHB1WPN7rrqGW6iyMnq32hvulhvotsm1h78xEcjawiIyOu14qzgVbXKClFV/JhLHlFzInmqhkJbJVSbpdSVgHzgPPqV6yaEfiYa65RY6YuSj6Q1hnaBbrtoBYqJqVk28Eyfw0dhwNOuVqLrDGHipmV/52bLZEI7219z3KM2Uv99Wz+OvGvPpeFXYKP4a4x6vmUVtQsfNHhDFA+RqLKytf8y/7YXvuRRqNs8vr4G5TUgjlnaHMa5ozVAycPhBqu4a2GlEw2HtPOgdem3HCs8Hi9Ubn90pOdVFR7uPMtze0V8skP+4Qq8yHMrsGgBLpExPzUmtpSC4l0V/ndavWcqKbQiEbJdwTMpnGxviyQi4QQa4QQbwshbKpX1R+BbvFQ1rWnlnHydnTWu0kZx3r5+yJ+9uTX9Lx3PvuO6Rfx9KfhvGetG5pLAmS19YXKAWw4vMH2WAXZBUzoNIGnJz7NtQOupWt2cJMT4ynA6EYztX+7Gn2epMAY5T7T7AdCdNEzERTgj9tL2FUSus3f0DZDAbiw54XcdsptgJb4FRZPFThc5KVpGaT11bQbNEs+KYrraMG6/Wz86bhPQV8xyr55DGhBBYGUlvuvZbNiP1IROsEq7qTnQnprayZsu0Gay+/AOjiuN5VppAXIGhvRKHm7KznQ6f0hUCClHAR8DrxiuyMhbhRCLBdCLD94MHZdemSAOKGs2Fha8qku7dQZkRPfbfVn6721vJj1e0tttyPLqnwDZf/bqr8FbZKuW8Sdsjpxx7A7bP3Axn6M6pqRWhoGYsRgH0/WO1FNvC90xmFgEksowoR/XvL8EsY9bhOiqZOTmsOiixcxc+hMX7JYVaTKhh43OF0MytM6Qd006Kbo5KwFHq8XRw2uowOllXTPy7C11s1cN8Z6Yyo+4r8RGjc+sJ+/SRju3Ah3bLSGA6e38l8PxmR+ev00VVdYiUbJFwNmyzwfsMyCSSlLpJSGj+QFwJqX7x/3vJRyuJRyeF5eXm3ktcWstHu0ybRYP2ZiFV0D/izF91ft5cVvd1iacjz12WbOfvoby/ifjlWwePNBaFWgVWm8VYuwCYzO+fvqvwNWV0M0RbY6ZmoPV9EmPwUi9LDIJG8FOFM0d02ox+lomjQjCLYFggnnVmqd1hohBMkObQI1Kkve6aLaU03HzI60TK0/S9FSoz8Md07WbpS7Dp+Mqvzs/ef241/XjPC9v2uKvxlJVnIWa69ey5wz5jBzaII0DLHD6dJyPsxuPVcGnHqj9tqw5JWSbxCi0QTLgJ5CiK5CiGRgBvCBeYAQwlxQZjpg73eoJ+4+U7P0fjG2K9mpSbaKY/CDC3n6Cy1zNBaWfIpuyX++YT8Pf7SeBev2BzXu9bltgPOf/Y6r9LaDFIy1LUJmxjzh+sDoB4LWzztnHi+d6e+pmZqUitvj5Y+faHXhw9aqsUOfTE3yVPot9Ru+1Cz6QKpDu1n8+xMhbwbmG9va4sgF5owomciWfBU4kxukSqPHXKM/DNOHaGGs5dWeqGuMj+7uV3524Zk/6/wz39NdQmP0tQWtpLAR5qv3VbBEoCnqjYhXnZTSDdwKLEBT3v+WUq4TQjwkhDCaZs4UQqwTQqwGZgLX1JfAduRkJFM0+xx+P60f2WkuSsutSv5AaQXHyqtxeyUOEZsGu3k2BakGd7JetMLk6fqpVAsbC9Xc5LoB11neGz7XJ8Y/QduM4Gp8/XP7M6yt9YHJOAYEl76NiG51uWQl0rDgnS4Ye2fwWLtyB8E7DLnGPPmYEyLG3IxLnwSOqOS9mrvmhPtE2E5ZNWHTT8eDSlh4vJK5S3f7KkqGw1yGI9okvLB1hhoT2SbbTwh/IbMi/Sm3EXZ+aoxEdTVJKT+RUvaSUnaXUj6qL7tfSvmB/vp3Usr+UsrBUsozpJTBfe4aiHbZqew4dMKnTD1eyS1v+Eu4xsKKB61e+MXDre0Du+VZ47vtWgSu2HnEougNt8ykzpMYlDvIt/x41XEAspND1253CAcX9byIZyY+A8C4P/t93DW+kZmy927w6wAAIABJREFUWKU5scrhgFm74fx/+JeNujnKndpb8hH7yJop3YvrkBYtEy77l+UvaYlmDhcnq0+S6coMPTZK3B4vZ85ZzC9fs3ZtKq+OXv6s1CTfHLQryvyCWBghCUlgtFNT/ZwJRhMxGfyM75VHaYWbNcXHWLX7KG8u282yIn8kQqyUPMCkvlYLu197q0K2U/Iznl/Cv77bEbQ8yZHE4DaDSU/So3Z0JR+pA9ADpz3A+E7jqXR7fOVp37l5dNhtbDH7TwPjl1Oz/XVEuk+EllEET4Vx15gbk0TslfvqeSS/pT3lhPXJf3Q7ANLhYuWBlTHJdjWejL4JqFFUWQMl73AI32TrgeO1qKzZ2Ok7HQZdor1uO8C6Tin5BqGRpM1FT34rTUkeOVHF9a8ur9djTe7XlqcvHcrMuSsBrVBVbqY/jd0bIiTa3GLPiIoRQpDiTPFZq+9seQeIrOQNig75/eS920Xo3GSH6Qcn7RqQGGnmVSei3WHINY8v2OQ/VqS52UObSdYnuatDlS4u8XcFW+jWFPLi4sXRiRmGfy+zT6oLF+tuhxGBVRQmZLTJcsn/+V9ntdOMhG1696jGltzVSGlyZ9lo1VcWohRwVIEhUSKEYPrgDrTT+6e2yUq1ZC2ardRckw8/NyuFA8cr2HqgjGv6XwNAh8wOJDuTcXvdvFz4Ml/t1lwvLZKjm5x6YqGmOAfnt4hYjMz+w/i38dpZwR2Gah2kzgyuKxMaU/KOV/KH9wspOnSCT9bu8x8rii8kWR9TVFpkP2DpC76Xx4ldAlSX1tqNrVOOtSSuobTvO6dv0DZ2VFRrMl1+anCJ4WaHoeBBKfkGosmd5Uy9VZ9ZkZipqRUWDc9fNYxzB3egoHU6T8/wxzKbFZj5Eb/K7WXM7C+Z9NTXnNv9XNZevZbs5GxfQtOTK7QOR+0z2kcdBnisvJrWGcm8d8uY2vl0TT84aVe90ZUG13+m1cWPan9Wd82GfaW88sNOJjyxCI9X+pLJwup4fWW67od6qfAl+3Et/cozJYb1aows1XSX9YH3mD6x3zVUS8UQ3DSue9RjF901gR9+NzHywEaNctc0BE1PyevJQAvX72+wYw7Kb8lfLx1KktPBgI4tePpSTdF7pWb1vbuy2FLj/f1Ve2wrZgYW1DJK7kaD2+Olb/vs2k/amSdevbFImQ8dJ++V/iSfsJa83igk3TTGtuqnOcU/RiV4zccxJz1JKXlsvhZX0Da7Zmn5nVtHH/ZYkJtB+xYRmmo0Rsbf43+tLPkGocmd5cBYdYOXr9USTIZ0qv9UakMnSCn5/XuF3P6mtVzvGlNsuFmZBJYLrkkTardX1q1OvvlY7gihitEQ4WZjTBKHbQFgOjczHFrynEd6YMXLsPMHbUXlcdi/3jcuo732pNG9RfRWsx1ur/UpxKiH9OoPO1m6Q8thCJxoV0SB+SasJl4bhCan5IUQ3Ht2sK90XM88Lh3ZiVln9al3GYwkGa+ETwt/CjvW3LYwMIEnPzM/cLgtUkpfNFGtMf3gqiojNCmPFpOSDpRtTI/W+pDQWt7tMbm4Dmrbu91V8OFt8K+psOFDeKI3rH5DG/Tzl2nRQXuKunvE3XUSPbBn8POLtcnd77dpE7szRnSKuqzBV3dN4Ku7JtRJniaD2XpXlnyD0CTP8g3julne3zG5Fw6H4LELBzGqW/2nUhu/fa+UFjfNgt+MCxpbZZoj6J3T27Iu2gJbxjGOnqx542w7th+upOhQtFE0obC6az5cba0HP1kPPw1lyXu9kutf9XcH6opWgdLzmKkZ9JtXQLVJzr7n+W4ade2BWq2HRt01RStL8MI3O7j5tRUsWLefU7vm8NiFwS38QtE1N6PG/vsmi8Wdpiz5hqBJKnmAZy7zT4BOG9Q+zMjYY/jFv9p0wBcj/dI1w+ndLjgc0qzk++T0YenlS33vu2SHrlho5uiJ2Ch3gwqSgxKAaox+DozEr/4drFFCRjcvO0t+64Eyuv2/T1iyzR+fbqgGd+AjfsHp/tcOh78Bdh0v7Wr9e8kylbGerz+VVbi9TTdhqb6xuGuarPpJKJrsWZ42qANFs89h9f1TgjJR6xvDXfPnTzdxrLya6YM7MLGPZrleMcoaRlcVUOYgzdTBvk16m6iOd/hkDHzoJvbJHDb+dNyStFRbet47n9eW7KTCbZ3MNWrr2FnyX2zQJs2FrrCXeXuRpN8MgiQqshaCM24adVHC5VUehj2iNaVOcgpfkTFFDDA/YSkl3yA0+bPcIr3he2EGumrN3YAeOX8gN5ncSVU2IZ0LLlrAe+e9F7Q8FEd1JW9+eqkVQy4HwKNfFi8sDs7MjR7jJEjue6+QioBSBskBlvynhT9Rro9p1yLVsofDMhunrvDLI/jBA0s314Yjppumy+EgN8s6IX7P1N6BmyiiRU28NjhNXsnHg8DqhIG13c3t+Dw2pmyHzA50bxl9dIhRC6ZHmzo+sXQ5DQCpXxZLtpeEGx2WQr2evmGN/2flHvq0y6KDrsCN0MnXf9zF8Ec+55evrWDO55sBv5Xfp532eY7ITA7oTU0+zNR92+38dX7M+DKI6+DvNdcWSnE5LFE0n8w8ndO659ptpogGiyWvlHxDoJR8fRBw7QY2aG5tqrwYiwRcIwMzVPho1Ojx8R6pXRaHyiq59Y3/UjDr45AZxHZs2X+cheuDW/W1zU7lwfMG0CYrhbZZmrL/eO0+XzVHYwLZSFh78n+0yc0+XTtz4XGtzWKq4cNPsS/3EAt3jVnJp7qcDO7UkmX3TqJo9jn066DCJutEYyiR3MRQSr4eWLPbWiPdSGs3yMnwP/6HCyGMFqMqol37uBqhd63aIdvhcgr2HC3nozVa5vC7K/ewYV8pry3ZGXE3ZgVrVrVfbz7I5H5tWXrvJFJsZH3jx10AVOr+e6Pk7pB+fWj1cy1MstrYY441goqZq4DYWPJvrSj2vTbOaV6WajodEzKjm2dSxA6l5OuBsT2tYZruAJeM05JBWffjGb7sOiv5nlO4zn0Pz3umMXVAe0tJ4N2HT3LeM99x33uFvuOFwukQvicUYXpWGdalle91ONd6mV7ALSPZuDwFyT0n45CSCmNDs7um3UDI0cNNpbH/2l/a5sJkqU2ltnuiYG4komgQ1BVcDwzrksOGh6Zy1WgtBDKwgYe5AXQs3DWGe6PO7hoh+MozGC8OcjOtJRaeX7zdFwl0tDx8NI/H60XaWNJtTNZwqK5KV774I2V6c3TfhLUQOJxOUqSk0tiuZAv0v9AQ3Le9NwYFygbm+7Oi63zjVFhJVu6ahkYp+XoiLdnJzJ/15KrRXbgsoPqg21SDOFaWvNMhat4NyobHLhhIbmYK5w/pGHJMtdte6GPl1SzdcdhSl8dsyZs7HrVK999EPrh1DNeP1Szxb7YcoqjkBMlJDlzGzVC3ylPNSn7E9WDU+jGXSdZP6KafjrNip1Z+4KtNB/h6c/SN408ztd9TSl7R2Gly9eQTidzMFB46b0DQcrN/N5pSu5E4UeUmNckRkwSdGSM7M2Nk+JK4gbH9Bje8spylRYcZ3yuPAbp1bZZoaGe/u8ZcrKtL6wzLPrcdLNOqifo6CWl7OeJ08mZ2Fv/T+Vb65PYCZ5JlPfh98r/7TyGyspSzB7TnY70iadHsc8J+LoPKavPEq7KDFI2bqK5gIcRUIcQmIcRWIcSsMOP+RwghhRDDYydi02NYlxx+M6knEBtLvujQCV+zlIbArk/t4ws2srRIs5y/3nzQZ7/fP60vFwzVngquGGXN4D1Pb3KdlZLEPVP9NYXWFB/T+gIYJyfg5jX1h74s23mEKsNGsb25CaTEp+BrQqUpccuc8apQNEYiKnkhhBN4FjgL6AdcKoToZzMuC62J94+xFrIp0lePvY5F8s7JKk+9Jn19e88ZtG/hr1I5d+ku3Lqif2v5bt5ftYdnv9oWsJWmeC8ens9TFw9m7QNTglovPv4/g1l+3yQcDkFGShJrH5jiW5eRnES4GYuf/+MH1hdqETXsXelbHi5aaUeU9Xhq2mhcoUhkorHkRwJbpZTbpZRVwDzgPJtxDwN/BpphI8ua48sHjYElX+n2WvzdseL9W8Yw+8KB5LdKZ2BHf+2ZV3/YyS9fW8G2g2Xc/fYabpu3KuQ+UpyaG8nOIk5Oclg6ZpnHFJWcMFny2me7bsB1+lpteaeqwBuL+aYZbN0b5RIiUemORT19RUh+8TlMfjjeUjQbotEMHQFzs8tifZkPIcRQoJOU8qMYytakMfznsVDyFdWeepkgHNyppc8/X1RitYI/33CAnz35dchtpamsQU0wavtUVHv9Pnn9XPnr62v7zMbfM9Wo8e4N8OObMTo6ReK1JbtqJLOihnQaAWNmxluKZkM0St7O4en75QohHMBfgDsj7kiIG4UQy4UQyw8ejD7aoSniaywSA3dNldtb71Egm/eX1Wi8r95LqLtY+VF49Xw4tsey+PZJWjGwM3rnQYBVniSMiVZNkf/o9fvxL35OayKydo9et17f9JxB7Vn9hylkpSRRGkHJSyl9biiFoqkQjZIvBjqZ3ucD5uLgWcAAYJEQoggYBXxgN/kqpXxeSjlcSjk8Ly+v9lI3AYy5wrCdkaKkotpTL+4aM9/ecwYTeufx82GhG5mcM7AGJZ3XvgXbv4JvnrQsbp2Zwlu/HM3frxgWNPHqS3ASmiJe2P/PQbs9csKI4Rfcd05fHjlvAC3SXGSnuTgaQck/sXATPe6d7zvk3BtU4o6i8RONZlgG9BRCdBVCJAMzgA+MlVLKY1LKXCllgZSyAFgCTJdSLq8XiZsIRtp9LMoaVLi99R7ql98qnZevHWn7xGDU6x/a2Z9EFNFd49EVrjPYVz+iIEc/jtUn7xRGcpQkPdlJSmZwK8cU/TwkJzm4/vRutNInTvccLef9VXvDnm/z5PH1Y7syunv9N5hRKOqbiJpBSukGbgUWABuAf0sp1wkhHhJCTK9vAZsqwueuqTuV1R5Skhomaefnw62W/ICO2Vw1ugCA03vm8ccLtKJivieUUErVqyv5cI23A/zr/m5PWvKXW1o9iQePV9JSjzL67RRrm8ep/bW6PKUV0RVai7a1n0KR6ERl/kkpP5FS9pJSdpdSPqovu19K+YHN2AnKio+Mf+K1cVjyBoPyW1pcNi3TkhnZNYei2efQu10Wwwu0hCe7sgYWNmlukfBK3t5dI4SXJIcIKtNcuOcYXj2bODPVGvo4dYCm5EvKKvF6JRc/90PYaBunKoOraCKodL44EasQSrfHi8crG8ySB8g0lU422hsauPRa8Gm+m47pA358J/xVn6rZpU2U+koT2GKdeD1wUitf/PPJ63A6RFDDlYPHK/Ea7f8CdHRrvRbPc19v51BZJUt3HA7b4jBUbR2ForGhyhrECUOJ1NWOr9AVXUOm33c3tVMM9NF3zc3gwen9uaBiMyzGehdb9k/tvzmixsYn7yPAks90acfdXbaFVNcE1hRbSzrvKN3CG3seAYKrULbL1sIv31y+2xcOatTYOXC8gnvfLbSMV+4aRVNBWfJxwhddU8fwmspqo/Z6w1ny3XIzfK+Lj5wMWn/1aQWmxCabz/cXU8J0OHdNwMTrNf2vAaBjVkfG9coLymB9rfg2vFI7H4F1fDq09PfO/VGPqTeY/tfv+Gy91XWjdLyiqaCUfJyoXapQMPGw5NuZShw8efHg6DZyV9ovFyK0z0pa3TUup4vBeYM5WnmUji3TfM1SwN8z1sAjreWQM1KS6N3W2k0qS3c7nbDpeqV88oqmglLycSJWGa/xsOS7tM7gwqEdee+WMaELo/nChyQUr4BHQnQE+vwBeOcX9utsCpRlJ2dzvOo48wuthceyUqxPBG3SgmP2F9w+zvLemLhVLf0UTRml5OOEobf+8fU2Hvlofa33Y7QWbEhL3ukQPHXJEIZ0Co5T92N6VlkcnLRkofAd8Npkmi55Vvt/3K/QXQ4X1d5qSwtFgJQMf37e8Q2zyUy2V9z/94uRvtcnqzycrHLbTrJ+uSm4R61C0RhRSj5OGGrl680H+ee3O3zNrGuKvx9qgjW3MBTnFw/B5k+D15/9hPX9ylf9rz1uWDQblr+kve8zzbcqyZGE2+vmnqm9LZunJVst+VDOlrE9ci3vfzpWEVQdE2D7wegqVioUiY5S8nEiMHrj/VV7Q4wMj2HJpyRqcwtDUQfSIqA8woe3QYmecfr1bFj0mPa6TT9o3d03zOV04fa6taYiJlJd2vnsmtkfCB0CGTghu+9YhW3jllg0c1EoEoEE1QxNn0AVVNvOfVf/aymQgJZ8KFvaiKZJzw1ed2iz9n/Zi/5lHmu9mSShWfJJTuulu+EnrTDZ+DaXa4eJcuJ037EKdh85yciCHMvyQItfoWisKCUfJwJ1UHZa7Zp+VMUhuiYq7JRs13Hg1SNZWnaG7I4w5VG4fZ22rGw/rHkLyk0hjqfeZNmF4a5xBTwJje+lKekqd+jDG7x54yg+njkWgGU7DrP7cLmvq5XBo3p5BoWisaOSoeJEeZV1orGubeYSr+G0jZa97C344New9t+Q2Qbu0Cec3Xq4Y+k+zVUD0HYAnP04dDnNsgtDyQda8r3apbF8F3g8RumD0JKd2k0rPNYq3cUXG+1LG6QnJ9r5bL5UV1dTXFxMRUXz6keUmppKfn4+LlfddINS8nFicKcWlvd1rWNe36WG68zP7gdXKpz/dzh3jlULJ+mlDQwFD3DRP6FN36DdpDhTqPBUkKz7tyZWPsG4fvmkOzQF4PY4AG9U7pp2LdLYsK/Udl2yM8HPZzOiuLiYrKwsCgoKYtKsvjEgpaSkpITi4mK6du1ap32pKzlOZKW6KJp9Dp/fMR6AqjoqeXMbvYTA/GP8w1E4Xe8p40yC5Izg8adcbX1vo+AB2qa3pdxdjkdombbbZQeOutohHNr5O1zmDjp8KDLCWOuqrEHiUFFRQevWrZuNggctQKB169YxeXpRSj7OGL70wyeqIoy0p1tuBucO7pCA7hqd3N7RadzpT0OqHnffMajfjA+jBWCVp4oxPTS3ixACoTcS+WiNFt8ejSVvDp189IIBnDu4Q2Q5FXGhOSl4g1h9ZqXk40zHlmmkuZzsOhxcAyYavDJiUd/4kKQ/WYStMhnA1R/AqF/BLz4LOcTl0PyTbq/b51IRgBBavoCU2s0uGkM8SXf5jOyaw+WndmFcTxVRowjNu+++ixCCjRs3Wpb/5S9/ITU1lWPH/AXzFi1aRIsWLRg6dCh9+/blwQcf9C2fNm0aDYlS8nFGCEHb7BR2Hy6v1faS6AzlBidNqytPaXH027QfDFMfA0foyzJJD8Gs9lb76tUIIRAOvY6NNJ5oorHkjbLIxo0hEU+kIlGYO3cuY8eOZd68eUHLR4wYwbvvvmtZfvrpp7Ny5UqWL1/Oa6+9xooVoUtb1ydKyScAwwtyWLnrSK0aiEiZoMrJsODbR1nALEoMJe/2uknWcwOEwNf31VDy7U1F1EKKqJ82w2VmnEa7DFhF86asrIzvvvuOF1980aLkt23bRllZGY888ghz58613TYjI4Nhw4axbds22/X1jYquSQAG5bfg7RXFvPx9EVeNLvApmRe/3UG33AzO6BOiuBcJ7K7J1v3b7QbFdLcWS97krgE9QF46yEh2kpES+dI2LHljPsNQ8n3aZYXaRBFnHvxwHev32kdE1ZZ+HbL5w7n9w4557733mDp1Kr169SInJ4f//ve/nHLKKcydO5dLL72U008/nU2bNnHgwAHatLH+XktKSliyZAm///3vOXjwYExlj4aoLHkhxFQhxCYhxFYhxCyb9b8UQqwVQqwSQnwrhOhntx+FPX3aacW0HvxwPe/81+/eePij9Vz78rKw20pJNJ6JhqfdQLhugRY6GUOShG7JS7fJXQOuJM2Sl9LJnBlDo9uXfjNNNZ4I9BMZ2O1KoZg7dy4zZswAYMaMGT6rfd68ecyYMQOHw8GFF17IW2+95dvmm2++YejQoUyZMoVZs2bRv3/4G0l9EdHcEUI4gWeByUAxsEwI8YGU0lw68Q0p5T/08dOBp4Cp9SBvk6RLa3+53iO1iLJJSHcNQOdRMd9lij6hW15dTkqS1ghEIHh+3RwAnKQzoGN0pYOdur9GuWsaD5Es7vqgpKSEL7/8ksLCQoQQeDwehBBcccUVbNmyhcmTJwNQVVVFt27duOWWWwDNJ//RRx81uLyBRGPJjwS2Sim3SymrgHnAeeYBUkrz81MGde+F0awwhz8WlQRH2ZRWVActM0hYd0090S5da8i9/+R+nyXvxX9+tjxyNu1bpNluG4jPkk823DVGw/DmdEYVkXj77be56qqr2LlzJ0VFRezevZuuXbvym9/8hgceeICioiKKiorYu3cve/bsYefOnfEW2UI0Sr4jsNv0vlhfZkEIcYsQYhvwZ2BmbMRrHphT6AObUwMcOxlaySfsxGs9YcTJv7f1PXYd1oqSFf70EwBO4axREpPRGcqY7163RwuB+3pzw/tNFYnL3LlzueCCCyzLLrroIoqKioKWX3DBBUHRN4F88cUX5Ofn+/5++OGHmMtsJpqJV7tfTZClLqV8FnhWCHEZcB9wdeAYIcSNwI0AnTt3rpmkTRiX08HYHrl8u/UQbpvmGSeqgtvTGXilTMwQynrCmHhdsm8JlDqA6Ww6sJ+MLJg9bnb4jQPolqs1Bt9fqmUVbtp/PKayKpoGixYtClo2c+ZMZs4MtmWfeuop3+sJEyYErZ8wYQLl5bULl64t0VjyxUAn0/t8IFzx83nA+XYrpJTPSymHSymH5+XlRS9lM+C160+le14Gbk+wp6uyOnTJg4SNk68njGQoAGeKZsGLpDIAWiS3sN0mFDkZWpincc5VCXlFUyQaJb8M6CmE6CqESAZmAB+YBwgheprengNsiZ2IzQeX00G1TQ0bu2UGUjavlG+zku+Wp1nirrRDAHTMDPIihmVMj1w65aRx8wStKUl+q+h8+QpFYyKikpdSuoFbgQXABuDfUsp1QoiH9EgagFuFEOuEEKuAO7Bx1Sgic7LKY1veoNrGujeQzWzi1XDXAKQlu3Ck7UQkHQGgZWq4nrPB5GWl8M1vJzKgo/YEcMfkXgCM6pYTbjOFolERVTKUlPIT4JOAZfebXt8WY7maJaHq14S15GnG7hrhIKPg77brakPrzBRevW4kg/NrdrNQKBIZVdYgAbn7rdWWEgd2k7EGUspmFV3jdPgjkXaXFVnWma382jKuVx4t0lUylKLpoJR8AvG/M4YA8NaKYl7/cZdveZU7tLvGKxMz4bUhOFRuDXU0smEVCoUfpeQTiPxW/szX+94r9L0OP/Eqm9XEayiSHEnqPCjqDSEEV155pe+92+0mLy/PVzZ4//79TJs2jcGDB9OvXz/OPvtsAIqKikhLS2PIkCG+v+eee873Ojk5mYEDBzJkyBBmzQqqGBMTlOmTQGSGKKoV1l1D8/LJA7w89WWu+fQay7JkRw3q1isUNSQjI4PCwkLKy8tJS0vjs88+o2NHfzTX/fffz+TJk7ntNm16cs2aNb513bt3Z9WqVZb93XST1qC+oKCAr776itzc+utloCz5BMLltNfW1WHcNVL6C2s1F4a1HRa0rEt2lzhIomhOnHXWWXz88ccAvuqTBvv27SM/P9/3ftCg2FZfrQvKkk8gAidQbzi9Ky98syNs/1dt4rW+JUtcpnQ6j4W73yc7JbqiZIpGzvxZ8NPa2O6z3UA4K3K29IwZM3jooYeYNm0aa9as4brrruObb74B4JZbbuGSSy7hmWeeYdKkSVx77bV06KCV2962bRtDhmjzbWPGjOHZZ5+NrfwRUEo+gchvlcaUfm1ZuH4/vzurDxcP78QL3+zAHUbJe2Xzc9cAvDL1FbYe3cr2Y9sBSE9Kj7CFQlE3Bg0aRFFREXPnzvX53A3OPPNMtm/fzqeffsr8+fMZOnQohYXavJqdu6YhUUo+gUhyOnj+Kn8T6+N69ckHPlxPn/bZjOrWOmgbSfOceD2l7Smc0vYUHl/2OABpSSpbtVkQhcVdn0yfPp277rqLRYsWUVJSYlmXk5PDZZddxmWXXca0adNYvHgxw4YFuxYbGuWTT2DSTCWIH/zQX75/3d5jFOoVEz1e2azrnxtx825v6CJuCkWsuO6667j//vsZOHCgZfmXX37JyZNaMuPx48fZtm1bwhRhVJZ8ApPk9N+DzclR5zz9LQBnD2xHtUf6Ohs1R05Waz+shTsXxlkSRXMgPz/fF0FjZsWKFdx6660kJSXh9Xq5/vrrGTFiBEVFRQ0vZABKyTcS8rJSgpZ9slarwmh0NmqO3DjoRt7c9CYvnflSvEVRNGHKysqClk2YMMFXTvjuu+/m7rvvDhpTUFDg883b0RA3gearHRoJD5+ntTsLVwbX3FmqudEmvQ1rr17LiHYj4i2KQpGQKCWf4Fw5uoCRBTl4vBIpJf3v/zRoTHe95K5CoVAEopR8I8Dh0CZYT1Z5OFHlsawb2TWHMT2Co24UCoUClJJvFDgdAo+UHK8IjiC5clSXZhlCqVAookMp+UaA0+HA7ZWUVQY39Fa1zxUKRTiUkm8EOAV4vZJSG0u+c2uV6alQKEKjlHwjQAhBWaXb1l2jUCjqn927d9O1a1cOHz4MwJEjR+jatSs7d+5k3bp1TJw4kV69etGzZ08efvhhX17Lyy+/jBCCL774wrevd999FyEEb7/9doPIHpWSF0JMFUJsEkJsFUIEFT0WQtwhhFgvhFgjhPhCCKFKAsaQLzceYMehEzy+YCMAC34zjqLZ51A0+5w4S6ZQNA86derEzTff7Kv5PmvWLG688UbatGnD9OnTmTVrFps3b2b16tV8//33/O1vf/NtO3DgQObOnet7P2/ePAYPHtxgskdU8kIIJ/AscBbQD7hUCNEvYNhKYLiUchDwNvDnWAuqgMI9pQCkJKkHMIWiobn99tvapjMWAAAI1ElEQVRZsmQJc+bM4dtvv+XOO+/kjTfeYMyYMUyZMgWA9PR0nnnmGWbP9tfYOf3001m6dCnV1dWUlZWxdetWX1XKhiCajNeRwFYp5XYAIcQ84DzAV0xFSvmVafwS4IpYCqmw0jlH+eEVzZM/Lf0TGw9vjOk+++T04Z6R90Qc53K5ePzxx5k6dSoLFy4kOTmZdevWBRUh6969O2VlZZSWakaZEIJJkyaxYMECjh07xvTp09mxY0dMP0M4ojEJOwK7Te+L9WWh+AUwvy5CKayc0tkaQeNoxgXJFIp4Mn/+fNq3b+8rVRCu/aZ5+YwZM5g3bx7z5s2zNBtpCKKx5O0+gW2SvRDiCmA4MD7E+huBG4GEqdDWGLjs1C78d9fReIuhUMSdaCzu+mLVqlV89tlnLFmyhLFjxzJjxgz69+/P4sWLLeO2b99OZmYmWVlZvmUjR46ksLCQtLQ0evXq1aByR2PJFwOdTO/zgb2Bg4QQk4B7gelSykq7HUkpn5dSDpdSDs/Ly6uNvM0Ss3umZxtVwkChaGiklNx8883MmTOHzp07c/fdd3PXXXdx+eWX8+233/L5558DUF5ezsyZM/ntb38btI/HHnuMP/7xjw0telRKfhnQUwjRVQiRDMwAPjAPEEIMBZ5DU/AHYi9m86ZVusv3+s2bRsdREoWiefLCCy/QuXNnJk+eDMCvfvUrNm7cyNKlS3n//fd55JFH6N27NwMHDmTEiBHceuutQfs466yzOOOMMxpadIQMV97QGCTE2cAcwAm8JKV8VAjxELBcSvmBEOJzYCCwT99kl5Ryerh9Dh8+XC5fvrxu0jcT9h0rZ/RjX9KxZRrfzZoYb3EUigZlw4YN9O3bN95ixAW7zy6EWCGlHB5ikyCiqicvpfwE+CRg2f2m15OiPaCi5rTNSuWm8d246JT8yIMVCoXChGoa0ghwOAS/O6t5WjIKhaJuqKwahUKhaMIoJa9QKBKeaOYOmxqx+sxKySsUioQmNTWVkpKSZqXopZSUlJSQmppa530pn7xCoUho8vPzKS4u5uDBg/EWpUFJTU0lP7/uwRZKySsUioTG5XLRtWvXeIvRaFHuGoVCoWjCKCWvUCgUTRil5BUKhaIJE1VZg3o5sBDHgRLgUIShLYBjDTQmtxnLk4gyKXnqPiYRZVLy1E2e3lLKrDDrrUgp4/IHLEerfRNp3PMNOKbZypOIMil5Yva9JpRMSp66yRONvOa/xuCu+bABx0RDU5WnJuNisZ/GeI6aqjyxPF5TPUeJJk/UxNNdsxxA1qCaWn0jhFiu5AlPosmk5IlMosmk5AlPJHlqKm884+Sfj+OxQ5FoMiWaPJB4Mil5IpNoMil5whNJnhrJGzdLXqFQKBT1T2PwySsUCoWittRkljaKWeFOwFfABmAdcJu+PAf4DNii/2+lLxfA08BWYA1wir68C7ACWKXv55fxlMe0v2xgD/BMvM+Rvs6jn6NVwAcJIE9nYKG+r/VAQRyvoTNM52YVUAGcH+fz82d9Hxv0MSIBvrM/AYX63yUNJE8f4AegErgrYF9TgU26rLMSQJ6XgANAYW1/87GUKdR+wh67LoLbfJD2ph9ZFrAZ6Kdf3LP05bOAP+mvzwbm6xfhKOBHfXkykKK/zgSKgA7xkse0v/8F3qBuSj5mMgFlifKd6esWAZNN31t6vL8z0w/pcDzlAU4DvkNroelE+wFPiPPv7Bw0xZIEZKCFNWc3gDxtgBHAo1gVmBPYBnRD0wGrgX7xkkdfNw44hbor+VidI9v9hD12XQSP4oO9D0xGuzO3Nwm5SX/9HHCpabxvnGlZa2AXtVDysZQHGAbMA66hDko+xjLVWcnHSh79gv02UeQJ2MeNwOtxPj+j0Z5O04B0NIXaN84y3Q3cZ1r+InBxfctjGvcAVgU2Glhgev874Hfxkse0vIA6KvlYyxS4n3DHqjefvBCiABgK/Ai0lVLuA9D/t9GHdQR2mzYr1pchhOgkhFijr/+TlHJvvOQRQjiAJ9F+FDGjrucISBVCLBdCLBFCnB9neXoBR4UQ/xFCrBRCPC6EcMZRHjMzgLl1kaWu8kgpf0B7zN6n/y2QUm6Ip0xolvJZQoh0IUQumourUwPIE4povsuGlKdeiJVMAfsJSb0oeSFEJvAO8BspZWm4oTbLJICUcreUchDQA7haCNE2jvL8CvhESrnbZn28ZALoLLV42cuAOUKI7nGUJwk4HbgL7TGzG9pTT7zkMfbTHhgILKitLLGQRwjRA+gL5KMprolCiHHxlElKuRD4BPge7Sb4A+BuAHlqJGcc5Yk5sZKpJvuJuZIXQrj0g78upfyPvni//mMzfnQH9OXFWC2HfMBisesW/Do0BRIveUYDtwohioAngKuEELNrI08MZTLODVLK7Wj+8KFxlKcYWCml3C6ldAPvofky4yWPwcXAu1LK6trIEkN5LgCWSCnLpJRlaD7yUXGWCSnlo1LKIVLKyWhKdksDyBOKiPqggeWJKbGSKcR+QhJTJS+EEGh+vQ1SyqdMqz4ArtZfX43mRzKWXyU0RgHHpJT7hBD5Qog0fZ+tgDFovqu4yCOlvFxK2VlKWYBmqb4qpZxVU3liKZMQopUQIkXfZy7aOVofL3mAZUArIUSePm5inOUxuJQ6uGpiKM8uYLwQIkn/kY5Hi5CIm0xCCKcQorW+z0HAILToqPqWJxTLgJ5CiK5CiGQ0N9sHcZQnZsRKpjD7CU2MJxPGoj1ercEfunY22uTpF2hWwhdAjj5eAM+izaivBYbryyfr+1it/78xnvIE7PMa6hZdE6tzdJr+frX+/xfxPkem720t8DKQHGd5CtBCXh0J8H050SZAjfDSpxJAplRdlvXAEmBIA8nTDs1qLwWO6q+z9XVno0WMbAPuTQB55qLNoVTryxvqd2YrU6j9hDu2ynhVKBSKJozKeFUoFIomjFLyCoVC0YRRSl6hUCiaMErJKxQKRRNGKXmFQqFowiglr1AoFE0YpeQVCoWiCaOUvEKhUDRh/j/rhEYZIBRjTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "corr = returns.rolling(125, min_periods=100).corr(spx_rets)\n",
    "corr.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### User-Defined Moving Window Functions\n",
    "#### The 'apply' method allows us to implement array functions over a moving window with help of 'rolling'.\n",
    "#### The only requirement is that the function produce a single value (i.e. reduction) from each piece of the array.\n",
    "#### eg - Computing sample quantiles using 'rolling().quantile()'.\n",
    "#### Another requirement may be to get perceentile rank of a particular value over the sample. This is achieved by 'scipy.stats.percentileofscore'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\adity\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: FutureWarning: Currently, 'apply' passes the values as ndarrays to the applied function. In the future, this will change to passing it as Series objects. You need to specify 'raw=True' to keep the current behaviour, and you can pass 'raw=False' to silence this warning\n",
      "  \"\"\"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x25843780438>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import percentileofscore\n",
    "\n",
    "score_at_2percent = lambda x: percentileofscore(x, 0.02)\n",
    "\n",
    "result = returns.AAPL.rolling(250).apply(score_at_2percent)\n",
    "\n",
    "result.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}