Fitted Trend Line and Residuals

[Sinansi]

Hello,

I see you have provided examples on predicting 12 intervals in the future. But I seek past values. Can you please give more examples on how to generate fitted line and residuals on a time series using arima and varima?

Thank you!

[fipelle]

Hi,

The code does not currently have a simple interface for producing in-sample predictions for the levels, using VARIMA models (it would require some small changes in the forecast function). However, it is quite easy to get the in-sample forecasts / residuals of the underlying VARMA models. Would that help?

[Sinansi]

Thanks for your reply!

I am not an expert with time series decomposition. Can you give a brief example on how to extract the trend (forecast) and residuals for in-sample (past data) using VARIMA?

[fipelle]

Hi,

Trend-cycle decompositions based on VARIMA models are not implemented yet. I would suggest you to take a look at the multivariate Beveridge and Nelson decomposition.

Alternatively, you could use any state-space model described in Harvey (1990). They are actually much easier to implement with the current status of the package. I am happy to give you more details on that if you can let me know which model would work best. An example is already reported in the Estimation of state-space models section in the readme.

--

Harvey, Andrew C. Forecasting, structural time series models and the Kalman filter. Cambridge university press, 1990.

[Sinansi]

@fipelle oh I was commenting at the same moment you were replying :)
I will have a look at it, and get back to you.

[fipelle]

Happy to help! I am currently updating the library offline. I will start again adding features relatively soon. The Beveridge and Nelson decomposition in on my list, but there is quite some stuff to add before that I am afraid.

PS: As mentioned, you can get the in-sample prediction and residuals for a VARMA (not a VARIMA). If that is what you actually want to do I can work out an example.

[fipelle]

I am moving it to a private todo list and closing the issue. I should get back to it soon. Please take a look at MessyTimeSeriesOptim.jl in the meantime, as I may implement it there.