ch5_Strategies.py

# -*- coding: utf-8 -*-
"""
Created on Tue Feb 22 20:55:00 2022

@author: user
"""

import talib
import kbars
import ShioajiLogin
import matplotlib.pyplot as plt
import pandas as pd
import numpy
import backtesttool
#從資料庫讀取小型台指歷史資料
df_MXFR1=kbars.readKbarsFromDB('MXFR1')
df_MXFR1=kbars.resampleKbars(df_MXFR1,period='1h')
close=df_MXFR1['Close']
high=df_MXFR1['High']
low=df_MXFR1['Low']
#選項:
#'MACD'
#'KD'
#'RSI'
#'BBAND'
#'PriceChannel'
#'Grid'
target='RSI'

#########################################
#5.1 MACD指標
###########################################
#製作MACD指標
#macd:快線,12日均線(EMA)-26日均線(EMA)
#macdsignal:慢線,快線的九天平均(EMA)
#macdhist:MACD柱,快線-慢縣
macd, macdsignal, macdhist =talib.MACD(close
           ,fastperiod=12 
           ,slowperiod=26 
           ,signalperiod=9)

if(target=='MACD'):
    ma_short=talib.EMA(close,12)
    ma_long=talib.EMA(close,26)
    plt.title('EMA(12)-EMA(26)')
    plt.plot((ma_short-ma_long)[-100:-1],color='green')
    plt.show()
    plt.title('macd')
    plt.plot(macd[-100:-1],color='green')
    plt.show()
    plt.title('macd-macdsignal')
    plt.plot((macd-macdsignal)[-100:-1],color='green')
    plt.show()
    plt.title('macdhist')
    plt.plot(macdhist[-100:-1],color='green')
    plt.show()
#使用快慢線交叉當作買賣訊號
def createSignalMACD(close,
                 periodFast,
                 periodSlow,
                 periodSignal):
    macd, macdsignal, macdhist =talib.MACD(close
       ,fastperiod=periodFast 
       ,slowperiod=periodSlow 
       ,signalperiod=periodSignal)
    ENABLESHORT=False
    #允許放空的訊號寫法
    if(ENABLESHORT): 
        BuySignal=(macdhist>0).astype(int)
        ShortSignal=(macdhist<0).astype(int)
        return BuySignal-ShortSignal    
    #不允許放空的訊號寫法，兩個差在允許放空的部分多了ShortSignal            
    else:
        BuySignal=(macdhist>0).astype(int)
        return BuySignal
#找出MACD買賣訊號的最佳化參數
def OptimizeMACD(
        df,
        rangeFast,#=numpy.arange(2,100,1,dtype=int)
        rangeSlow,#=numpy.arange(2,100,1,dtype=int)
        rangeSignal#=numpy.arange(2,100,1,dtype=int)
        ):

    openPrice=df['Open']
    closePrice=df['Close']  
    bestret=0
    bestret_series=[]
    bestperiodFast=0
    bestperiodSlow=0
    bestperiodSignal=0
    for periodFast in rangeFast:
        for periodSlow in rangeSlow:
            for periodSignal in rangeSignal:
                print("periodFast:"+str(periodFast))
                print("periodSlow:"+str(periodSlow))
                print("periodSignal:"+str(periodSignal))
                #錯誤檢查,快線週期要比慢線短
                if(periodFast>=periodSlow):
                    continue
                #製作買賣訊號
                BuySignal=createSignalMACD(closePrice,
                                       periodFast,
                                       periodSlow,
                                       periodSignal)
                #對訊號進行回測
                retStrategy,ret_series=backtesttool.backtest_signal(
                    openPrice
                    ,BuySignal)
                #如果結果比之前更好,就記錄下來
                if(bestret<retStrategy):
                    bestret=retStrategy
                    bestret_series=ret_series
                    bestperiodFast=periodFast
                    bestperiodSlow=periodSlow
                    bestperiodSignal=periodSignal
                    
    return bestret,bestret_series,(bestperiodFast,bestperiodSlow,bestperiodSignal)

if(target=='MACD'):
    #最佳化Fast,Slow,Signal
    rangeFast=numpy.arange(2,100,1,dtype=int)
    rangeSlow=numpy.arange(2,100,1,dtype=int)
    rangeSignal=numpy.arange(2,100,1,dtype=int)
    bestret,bestret_series,parameters=OptimizeMACD(
            df_MXFR1,
            rangeFast,#=numpy.arange(2,100,1,dtype=int)
            rangeSlow,#=numpy.arange(2,100,1,dtype=int)
            rangeSignal#=numpy.arange(2,100,1,dtype=int)
            )
    print('MACD bestret:'+str(bestret))
    print('MACD MDD:'+str(backtesttool.calculateMDD(bestret_series)))
    
    plt.plot(numpy.log10(
        backtesttool.prefixProd(bestret_series))
        ,color='green')
    plt.title('MACD Profit(log)')
    plt.show()

#########################################
#5.2 KD指標
###########################################

#裡面的參數是預設值,如果把fastk_period的數值改成9就是坊間使用的KD指標設定
#RSV線:(收盤價-最近a天最低價)/(最近a天最高價-最近a天最低價), a=fastk_period
#slowk為K值=k天RSV平均,b=slowk_period
#slowd為D值=d天slowk平均,c=slowd_period
#K往上穿越D為黃金交叉,做多
#K往下穿越D為死亡交叉,做空
slowk, slowd = talib.STOCH(high, low, close,
                     fastk_period=5,
                     slowk_period=3, 
                     slowk_matype=talib.MA_Type.SMA,
                     slowd_period=3,
                     slowd_matype=talib.MA_Type.SMA
                     )

if(target=='KD'):
    rollingHigh=high.rolling(5).max()
    rollingLow=low.rolling(5).min()
    RSV=(close-rollingLow)/(rollingHigh-rollingLow)
    plt.plot(talib.SMA(RSV,3)[-100:-1])
    plt.title('SMA(RSV,3)')
    plt.show()
    plt.plot(slowk[-100:-1])
    plt.title('slowk')
    plt.show()
    plt.plot(talib.SMA(slowk,3)[-100:-1])
    plt.title('SMA(slowk,3)')
    plt.show()
    plt.plot(slowd[-100:-1])
    plt.title('slowd')
    plt.show()
    plt.plot((slowk-slowd)[-100:-1])
    plt.title('KD signal(slowk-slowd)')
    plt.show()
#使用KD交叉當作買賣訊號
def createSignalKD(high,low,close,
                 fastk=5,
                 slowk=3,
                 slowd=3):
    slowk, slowd = talib.STOCH(high, low, close,
                     fastk_period=fastk,
                     slowk_period=slowk, 
                     slowk_matype=talib.MA_Type.SMA,
                     slowd_period=slowd,
                     slowd_matype=talib.MA_Type.SMA
                     )
    ENABLESHORT=False
    #允許放空的訊號寫法
    if(ENABLESHORT): 
        BuySignal=(slowk>slowd).astype(int)
        ShortSignal=(slowk<slowd).astype(int)
        return BuySignal-ShortSignal    
    #不允許放空的訊號寫法，兩個差在允許放空的部分多了ShortSignal            
    else:
        BuySignal=(slowk>slowd).astype(int)
        return BuySignal
#找出KD買賣訊號的最佳化參數
def OptimizeKD(
        df,
        range_fastk,#=numpy.arange(2,100,1,dtype=int)
        range_slowk,#=numpy.arange(2,100,1,dtype=int)
        range_slowd#=numpy.arange(2,100,1,dtype=int)
        ):

    openPrice=df['Open']
    closePrice=df['Close']  
    highPrice=df['High']  
    lowPrice=df['Low']  
    bestret=0
    bestret_series=[]
    best_fastk=0
    best_slowk=0
    best_slowd=0
    for fastk in range_fastk:
        for slowk in range_slowk:
            for slowd in range_slowd:
                print("fastk:"+str(fastk))
                print("slowk:"+str(slowk))
                print("slowd:"+str(slowd))
                
                #製作買賣訊號
                BuySignal=createSignalKD(highPrice,lowPrice,closePrice,
                                       fastk,
                                       slowk,
                                       slowd)
                #對訊號進行回測
                retStrategy,ret_series=backtesttool.backtest_signal(
                    openPrice
                    ,BuySignal)
                #如果結果比之前更好,就記錄下來
                if(bestret<retStrategy):
                    bestret=retStrategy
                    bestret_series=ret_series
                    best_fastk=fastk
                    best_slowk=slowk
                    best_slowd=slowd
                    
    return bestret,bestret_series,(best_fastk,best_slowk,best_slowd)

if(target=='KD'):
    #最佳化fastk,slowk,slowd
    range_fastk=numpy.arange(2,100,1,dtype=int)
    range_slowk=numpy.arange(2,100,1,dtype=int)
    range_slowd=numpy.arange(2,100,1,dtype=int)
    bestret,bestret_series,parameters=OptimizeKD(
        df_MXFR1,
        range_fastk,
        range_slowk,
        range_slowd
        )
    print('KD bestret:'+str(bestret))
    print('KD MDD:'+str(backtesttool.calculateMDD(bestret_series)))
    plt.plot(numpy.log10(
        backtesttool.prefixProd(bestret_series))
        ,color='green')
    plt.title('KD Profit(log)')
    plt.show()

#########################################
#5.3 RSI指標
###########################################
#定義為n日內漲幅平均值/(n日內跌幅平均值+n日內漲幅平均值)
real = talib.RSI(close, timeperiod=14)  
if(target=='RSI'):
    #計算漲跌幅,並且把漲幅寫到pos,把跌幅寫到neg
    pos=close.copy()-close.shift(1)
    neg=close.copy()-close.shift(1)
    pos[0]=pos[1]
    neg[0]=neg[1] 
    pos[pos<0]=0
    neg[neg>0]=0
    #轉成絕對值,拿掉正負號
    pos=pos.abs()
    neg=neg.abs()
    #算平均值
    posSMA=talib.SMA(pos,14)
    negSMA=talib.SMA(neg,14)
    RSI=posSMA/((posSMA+negSMA))   
    plt.plot(RSI[-100:-1]*100)
    plt.title('RSI(implement with SMA)')
    plt.show()
    plt.plot(real[-100:-1])
    plt.title('real')
    plt.show()
    #https://en.wikipedia.org/wiki/Moving_average#Modified_moving_average
    def SMMA(s_in,period):
        s_out=s_in.copy()
        for i in range(1,s_in.size,1):
            if(i<period):
                s_out[i]=s_out[i-1]*i/(i+1)+s_in[i]/(i+1)
            else:
                s_out[i]=s_out[i-1]*(period-1)/(period)\
                    +s_in[i]/(period)
        return s_out
    posSMMA=SMMA(pos,14)
    negSMMA=SMMA(neg,14)
    RSI=posSMMA/((posSMMA+negSMMA))  
    plt.plot(RSI[-100:-1]*100)
    plt.title('RSI(SMMA)')
    plt.show()
    
    real2 = talib.RSI(close[-100:-1], timeperiod=14)
    plt.plot(real[-80:-1],'green')
    plt.plot(real2[-80:-1],'red')
    plt.title('original RSI vs RSI with only 100 kbars as input')
    plt.show()
#使用RSI往上穿越longTH做多,往下穿越shortTH做空的買賣策略
#longTH>shortTH,longTH預設值為70,shortTH預設值為30
def createSignalRSI(close,
                 timeperiod=14,          longTH=70,
                 shortTH=30):
    real = talib.RSI(close, timeperiod=timeperiod)  

    ENABLESHORT=False
    if(ENABLESHORT):
        BuySignal=(real>longTH).astype(int)
        ShortSignal=(real<shortTH).astype(int)
        return BuySignal-ShortSignal
    else:
        BuySignal=(real>longTH).astype(int)
        return BuySignal
#找出RSI買賣訊號的最佳化參數
def OptimizeRSI(
        df,
        range_period,#=numpy.arange(2,100,1,dtype=int)
        range_longTH,#=numpy.arange(2,100,1,dtype=int)
        range_shortTH#=numpy.arange(2,100,1,dtype=int)
        ):

    openPrice=df['Open']
    closePrice=df['Close']  
    bestret=0
    bestret_series=[]
    best_period=0
    best_longTH=0
    best_shortTH=0
    for period in range_period:
        for longTH in range_longTH:
            for shortTH in range_shortTH:
                print("period:"+str(period))
                print("longTH:"+str(longTH))
                print("shortTH:"+str(shortTH))
                if(longTH<=shortTH):
                    continue
                #製作買賣訊號
                BuySignal=createSignalRSI(closePrice,
                                       period,
                                       longTH,
                                       shortTH)
                #對訊號進行回測
                retStrategy,ret_series=backtesttool.backtest_signal(
                    openPrice
                    ,BuySignal)
                #如果結果比之前更好,就記錄下來
                if(bestret<retStrategy):
                    bestret=retStrategy
                    bestret_series=ret_series
                    best_period=period
                    best_longTH=longTH
                    best_shortTH=shortTH
                    
    return bestret,bestret_series,(best_period,best_longTH,best_shortTH)

if(target=='RSI'):
    #最佳化period,longTH,shortTH
    range_period=numpy.arange(2,100,1,dtype=int)
    range_longTH=numpy.arange(0,100,1,dtype=int)
    range_shortTH=numpy.arange(0,100,1,dtype=int)
    bestret,bestret_series,parameters=OptimizeRSI(
        df_MXFR1,
        range_period,
        range_longTH,
        range_shortTH
        )
    print('RSI bestret:'+str(bestret))
    print('RSI MDD:'+str(backtesttool.calculateMDD(bestret_series)))
    plt.plot(numpy.log10(
        backtesttool.prefixProd(bestret_series))
        ,color='green')
    plt.title('RSI Profit(log)')
    plt.show()

#########################################
#5.4 布林通道
###########################################
upperband, middleband, lowerband = \
    talib.BBANDS(close, 
                 timeperiod=5,
                 nbdevup=2,
                 nbdevdn=2, 
                 matype=talib.MA_Type.SMA)
    
if(target=='BBAND'):    
    timeperiod=20
    SmallStdDev=1.0
    LargeStdDev=2.0
    upperband_Small, middleband_Small, lowerband_Small = \
        talib.BBANDS(close, 
                     timeperiod=timeperiod,
                     nbdevup=SmallStdDev,
                     nbdevdn=SmallStdDev, 
                     matype=talib.MA_Type.SMA)
    upperband_Large, middleband_Large, lowerband_Large = \
        talib.BBANDS(close, 
                     timeperiod=timeperiod,
                     nbdevup=LargeStdDev,
                     nbdevdn=LargeStdDev, 
                     matype=talib.MA_Type.SMA)
    plt.plot(middleband_Small[-200:-1]
        ,color='green')
    plt.plot(upperband_Small[-200:-1]
        ,color='blue')
    plt.plot(lowerband_Small[-200:-1]
        ,color='blue')
    plt.plot(lowerband_Large[-200:-1]
        ,color='red')
    plt.plot(upperband_Large[-200:-1]
        ,color='red')
    plt.title('BollingerBand Example')
    plt.show()
#這邊的布林通道交易訊號使用以下連結的
#https://www.investopedia.com/trading/using-bollinger-bands-to-gauge-trends/#:~:text=Bollinger%20Bands%C2%AE%20are%20a%20trading%20tool%20used%20to%20determine,lot%20of%20other%20relevant%20information.
#Create Multiple Bands for Greater Insight
def createSignalBBAND(close,
                 timeperiod=20,
                 SmallStdDev=1.0,
                 LargeStdDev=2.0):
    upperband_Small, middleband_Small, lowerband_Small = \
        talib.BBANDS(close, 
                     timeperiod=timeperiod,
                     nbdevup=SmallStdDev,
                     nbdevdn=SmallStdDev, 
                     matype=talib.MA_Type.SMA)
    upperband_Large, middleband_Large, lowerband_Large = \
        talib.BBANDS(close, 
                     timeperiod=timeperiod,
                     nbdevup=LargeStdDev,
                     nbdevdn=LargeStdDev, 
                     matype=talib.MA_Type.SMA)    
    ENABLESHORT=True
    #允許放空的訊號寫法
    if(ENABLESHORT): 
        BuySignal=((close>=upperband_Small) & (close<=upperband_Large)).astype(int)
        ShortSignal=((close>=lowerband_Large) & (close<=lowerband_Small)).astype(int)
        return BuySignal-ShortSignal    
    #不允許放空的訊號寫法，兩個差在允許放空的部分多了ShortSignal            
    else:
        BuySignal=((close>=upperband_Small) & (close<=upperband_Large)).astype(int)
        return BuySignal    
#找出BBAND買賣訊號的最佳化參數
def OptimizeBBAND(
        df,
        range_period,#=numpy.arange(2,100,1,dtype=int)
        range_SmallStdDev,#=numpy.arange(0.5,5,0.5,dtype=float)
        range_LargeStdDev#=numpy.arange(0.5,5,0.5,dtype=float)
        ):

    openPrice=df['Open']
    closePrice=df['Close']  
    bestret=0
    bestret_series=[]
    best_period=0
    best_SmallStdDev=0
    best_LargeStdDev=0
    for period in range_period:
        for SmallStdDev in range_SmallStdDev:
            for LargeStdDev in range_LargeStdDev:
                print("period:"+str(period))
                print("SmallStdDev:"+str(SmallStdDev))
                print("LargeStdDev:"+str(LargeStdDev))
                if(LargeStdDev<=SmallStdDev):
                    continue
                #製作買賣訊號
                BuySignal=createSignalBBAND(closePrice,
                                       timeperiod=period,
                                       SmallStdDev=SmallStdDev,
                                       LargeStdDev=LargeStdDev)
                #對訊號進行回測
                retStrategy,ret_series=backtesttool.backtest_signal(
                    openPrice
                    ,BuySignal)
                #如果結果比之前更好,就記錄下來
                if(bestret<retStrategy):
                    bestret=retStrategy
                    bestret_series=ret_series
                    best_period=period
                    best_SmallStdDev=SmallStdDev
                    best_LargeStdDev=LargeStdDev
                    
    return bestret,bestret_series,(best_period,best_SmallStdDev,best_LargeStdDev)

if(target=='BBAND'):
    #最佳化period,SmallStdDev,LargeStdDev
    range_period=numpy.arange(2,100,1,dtype=int)
    range_SmallStdDev=numpy.arange(0.5,3,0.1,dtype=float)
    range_LargeStdDev=numpy.arange(0.5,3,0.1,dtype=float)
    bestret,bestret_series,parameters=OptimizeBBAND(
        df_MXFR1,
        range_period,
        range_SmallStdDev,
        range_LargeStdDev
        )
    print('BBAND bestret:'+str(bestret))
    print('BBAND MDD:'+str(backtesttool.calculateMDD(bestret_series)))
    plt.plot(numpy.log10(
        backtesttool.prefixProd(bestret_series))
        ,color='green')
    plt.title('BBAND Profit(log)')
    plt.show()
#########################################
#5.5 價格通道
###########################################
#價格通道就是過去一段時間的最高價和最低價組成的通道線
#當最高價創新高的時候做多,最低價創新低的時候做空

if(target=='PriceChannel'):    
    period=20
    channel_high=high.rolling(period).max()
    channel_low=low.rolling(period).min()

    plt.plot(close[-50:-1]
        ,color='green')
    plt.plot(channel_high[-50:-1]
        ,color='blue')
    plt.plot(channel_low[-50:-1]
        ,color='blue')
    plt.plot(high[-50:-1]
        ,color='red'
        , marker='o')
    plt.plot(low[-50:-1]
        ,color='green'
        , marker='o')
    plt.title('PriceChannel Example')
    plt.show()
def createSignalPriceChannel(
        df,period):
    high=df['High']
    low=df['Low']
    #創新高買進訊號
    BuySignal=(high==high.rolling(period).max()).astype(int)
    #創新低買進訊號
    SellSignal=(low==low.rolling(period).min()).astype(int)
    signal=BuySignal-SellSignal
    #上面的買賣訊號只有在穿過通道線的時候才有值,這邊用一些小技巧把中間的數值也填上去
    signal[signal==0]=float("NaN")
    signal[0]=0
    signal=signal.fillna(method="ffill")
    ENABLESHORT=False
    if(not ENABLESHORT):
        signal[signal<0]=0
    return signal
#找出價格通道買賣訊號的最佳化參數
def OptimizePriceChannel(
        df,
        range_period#=numpy.arange(2,100,1,dtype=int)
        ):
    openPrice=df['Open']
    closePrice=df['Close']  
    bestret=0
    bestret_series=[]
    best_period=0
    for period in range_period:
        print("period:"+str(period))
        #製作買賣訊號
        BuySignal=createSignalPriceChannel(df,period)
        #對訊號進行回測
        retStrategy,ret_series=backtesttool.backtest_signal(
            openPrice
            ,BuySignal)
        #如果結果比之前更好,就記錄下來
        if(bestret<retStrategy):
            bestret=retStrategy
            bestret_series=ret_series
            best_period=period
            
    return bestret,bestret_series,(best_period)

if(target=='PriceChannel'):
    #最佳化period
    range_period=numpy.arange(2,1000,1,dtype=int)
    bestret,bestret_series,parameters=OptimizePriceChannel(
        df_MXFR1,
        range_period
        )
    print('PriceChannel bestret:'+str(bestret))
    print('PriceChannel MDD:'+str(backtesttool.calculateMDD(bestret_series)))
    plt.plot(numpy.log10(
        backtesttool.prefixProd(bestret_series))
        ,color='green')
    plt.title('PriceChannel Profit(log)')
    plt.show()
#########################################
#5.6. 網格交易策略
###########################################

#根據乖離率低買高賣的策略
#在加密貨幣試過現成的網格交易機器人,感覺滿有意思的,所以寫了自己的版本
def createGridSignal(df,
                     BiasUpperLimit,
                     UpperLimitPosition,
                     BiasLowerLimit,
                     LowerLimitPosition,
                     BiasPeriod):

    close=df['Close']
    
    Bias=close/close.rolling(window=BiasPeriod).mean()
    Bias=Bias.fillna(method='bfill')
    
    positiondiff=UpperLimitPosition-LowerLimitPosition
    biasdiff=BiasUpperLimit-BiasLowerLimit
    position=LowerLimitPosition+(Bias-BiasLowerLimit)*positiondiff/biasdiff
    position[Bias<=BiasLowerLimit]=LowerLimitPosition
    position[Bias>=BiasUpperLimit]=UpperLimitPosition
    return position
def OptimizeGrid(
        df,
        range_BiasUpper,#=numpy.arange(1.0,2.0,0.1,dtype=float)
        range_UpperPosition,#=numpy.arange(0.1,0.5,0.1,dtype=float)        
        range_BiasLower,#=numpy.arange(0.5,1.0,0.1,dtype=float)
        range_LowerPosition,#=numpy.arange(0.5,1.0,0.1,dtype=float)
        range_period #=numpy.arange(2,100,1,dtype=int)
        ):
    openPrice=df['Open']
    closePrice=df['Close']  
    bestret=0
    bestret_series=[]
    best_BiasUpper=0
    best_UpperPosition=0
    best_BiasLower=0
    best_LowerPosition=0
    best_period=0
    for BiasUpper in range_BiasUpper:
        for UpperPosition in range_UpperPosition:
            for BiasLower in range_BiasLower:
                for LowerPosition in range_LowerPosition:
                    for period in range_period:
                        print("BiasUpper:"+str(BiasUpper))
                        print("UpperPosition:"+str(UpperPosition))
                        print("BiasLower:"+str(BiasLower))
                        print("LowerPosition:"+str(LowerPosition))
                        print("period:"+str(period))
                        if(BiasUpper<=BiasLower):
                            continue
                        if(UpperPosition>=LowerPosition):
                            continue
                        
                        #製作買賣訊號
                        BuySignal=createGridSignal(df,
                             BiasUpper,
                             UpperPosition,
                             BiasLower,
                             LowerPosition,
                             period)
                        #對訊號進行回測
                        retStrategy,ret_series=backtesttool.backtest_signal(
                            openPrice
                            ,BuySignal)
                        #如果結果比之前更好,就記錄下來
                        if(bestret<retStrategy):
                            bestret=retStrategy
                            bestret_series=ret_series
                            best_BiasUpper=BiasUpper
                            best_UpperPosition=UpperPosition
                            best_BiasLower=BiasLower
                            best_LowerPosition=LowerPosition
                            best_period=period
            
    return bestret,bestret_series,\
        (best_BiasUpper,best_UpperPosition,best_BiasLower,best_LowerPosition,best_period)

if(target=='Grid'):
    import yfinance as yf    
    tw = yf.Ticker("0052.tw")
    TW_hist = tw.history(period="5y")
    us = yf.Ticker("00662.tw")
    US_hist = us.history(period="5y")
    #兩邊歷史資料長度不一樣,取交集
    idx = numpy.intersect1d(TW_hist.index, US_hist.index)
    TW_hist = TW_hist.loc[idx]
    US_hist = US_hist.loc[idx]
   
    
    TW_open=TW_hist['Open']
    TW_close=TW_hist['Close']
    TW_high=TW_hist['High']
    TW_low=TW_hist['Low']
    
    US_open=US_hist['Open']
    US_close=US_hist['Close']
    US_high=US_hist['High']
    US_low=US_hist['Low']
    
    kbars = pd.DataFrame(\
        {'ts':TW_close.index\
        ,'Close':TW_close/US_close\
        ,'Open':TW_open/US_open\
        ,'High':TW_high/US_low\
        ,'Low':TW_low/US_high}).dropna() 
    #最佳化 BiasUpper,BiasLower,period
    range_BiasUpper=numpy.arange(1.0,2.0,0.1,dtype=float)
    range_UpperPosition=numpy.arange(0.1,0.2,0.1,dtype=float)        
    range_BiasLower=numpy.arange(0.5,1.0,0.1,dtype=float)
    range_LowerPosition=numpy.arange(0.9,1.0,0.1,dtype=float)
    range_period=numpy.arange(2,100,1,dtype=int)
    bestret,bestret_series,parameters=OptimizeGrid(
        kbars,
        range_BiasUpper,
        range_UpperPosition,
        range_BiasLower,
        range_LowerPosition,
        range_period
        )
    (best_BiasUpper,\
     best_UpperPosition,\
     best_BiasLower,\
     best_LowerPosition,\
     best_period)=parameters
    
    #最佳化 range_UpperPosition,range_LowerPosition,range_period
    range_BiasUpper=numpy.arange(best_BiasUpper,best_BiasUpper+0.1,0.1,dtype=float)
    range_UpperPosition=numpy.arange(0.1,0.5,0.1,dtype=float)        
    range_BiasLower=numpy.arange(best_BiasLower,best_BiasLower+0.1,0.1,dtype=float)
    range_LowerPosition=numpy.arange(0.5,1.0,0.1,dtype=float)
    range_period=numpy.arange(2,100,1,dtype=int)
    bestret,bestret_series,parameters=OptimizeGrid(
        kbars,
        range_BiasUpper,
        range_UpperPosition,
        range_BiasLower,
        range_LowerPosition,
        range_period
        )
    (best_BiasUpper,\
     best_UpperPosition,\
     best_BiasLower,\
     best_LowerPosition,\
     best_period)=parameters
        
    
    #最佳化 BiasUpper,BiasLower,range_period
    range_BiasUpper=numpy.arange(1.0,2.0,0.1,dtype=float)
    range_UpperPosition=numpy.arange(best_UpperPosition,best_UpperPosition+0.1,0.1,dtype=float)        
    range_BiasLower=numpy.arange(0.5,1.0,0.1,dtype=float)
    range_LowerPosition=numpy.arange(best_LowerPosition,best_LowerPosition+0.1,0.1,dtype=float)
    range_period=numpy.arange(2,100,1,dtype=int)
    bestret,bestret_series,parameters=OptimizeGrid(
        kbars,
        range_BiasUpper,
        range_UpperPosition,
        range_BiasLower,
        range_LowerPosition,
        range_period
        )
    
    
    ### 跨市網格交易報酬計算 ###    
    (best_BiasUpper\
    ,best_UpperPosition\
    ,best_BiasLower\
    ,best_LowerPosition\
    ,best_period)=parameters
    
    position=createGridSignal(kbars,
                     best_BiasUpper,
                     best_UpperPosition,
                     best_BiasLower,
                     best_LowerPosition,
                     best_period)
    buyTW=position
    buyUS=1.0-position
    
    retTW,retseriesTW=backtesttool.backtest_signal(TW_open,buyTW,tradecost=0.0000176)
    retUS,retseriesUS=backtesttool.backtest_signal(US_open,buyUS,tradecost=0.0000176)
    retseries=(retseriesTW-1.0)+(retseriesUS-1.0)+1.0
    prefixProfit=backtesttool.prefixProd(retseries)
    #plt.plot(buyTW,color='red')
    print('strategyMDD:',backtesttool.calculateMDD(retseries))
    print('USMDD:',backtesttool.calculateMDD_fromClose(US_close))
    print('TWMDD:',backtesttool.calculateMDD_fromClose(TW_close))
    print('strategyProfit:',(prefixProfit.tolist()[-1]/prefixProfit.tolist()[0])-1)
    print('USProfit:',(US_close.tolist()[-1]/US_close.tolist()[0])-1)
    print('TWProfit:',(TW_close.tolist()[-1]/TW_close.tolist()[0])-1)
    plt.plot(numpy.log10(
        backtesttool.prefixProd(retseries))
        ,color='green')
    plt.title('Grid Profit(log)')
    plt.show()