ARIMA model for a large data set

[Jacek Strupinski]

Hello,

I'm doing an analysis of a movement of an object in time (Position X, Y, and Z). I'm trying to do forecasting and predict ARIMA models. However, I have 3000 observations (24 per second).

I encountered two problems:
1) How to time set the time variable in my example? What I have is a specific time stamp like...4.27s, 4.28s, 4.29s... etc. and I'm not sure how to convert it properly.
2) How to calculate ARIMAs at this number of observations? 750 lags make it impossible to calculate manually.

I would very appreciate your help and suggestions.

Best,
Jacek

[Ashish Tyagi]

Hi Jacek,

For (1), tsset time variable does not need to be a date/time format variable. You can carefully sort the data in chronological order and then generate an observation number series through gen time = _n. For (2), does your ACF/PACF really suggests a model with 750 lags? If so, then Stata's arima is impossible indeed. You might want to check out high-dimensional time series models using LASSO and Stata's Lassopack.

[Jacek Strupinski]

Hi Ashish,

Thanks for your answer. I'll try your suggestion to (1), it should work. For (2), I picked 750 according to 25% rule of all observations. The data differ quite a lot and I thought just a small part of it won't be sufficient to predict accurately for the whole set. Is this wrong and I should pick a smaller number of lags?

[Ashish Tyagi]

Hi Jacek,

I have never heard of the 25% rule but it could be something specific to your field. Box-Jenkins method of parsimonious model selection based on autocorrelations and partial autocorrelations functions is a widely accepted method to select lags and might help you get rid of irrelevant lag terms in the ARIMA model. For a good explanation of it, refer to Ch 2 in Walter Enders Textbook "Applied Econometric Time Series" (2014).