Time-Series – Estimating the Same Model Over Multiple Time Series: A Comprehensive Guide

time series

I have a novice background in time series (some ARIMA estimation/forecasting) and am facing a problem I don't fully understand. Any help would be greatly appreciated.

I am analyzing multiple time series, all over the same time interval and all of the same frequency, all describing a similar type of data. Each series is just one variable, there are no other corresponding predictors that I'm looking at.

I have been asked to estimate a single model that describes ALL the series – for example, imagine I could find one ARIMA (p,d,q) with the same orders, coefficients, etc. that could fit all the series. My supervisor does not want me to separately estimate each series, nor does he want me to do some sort of VAR model with dependencies between the series.

My question is: what would I even call such a model, and how might I go about estimating / forecasting it? If it's easier for you to use code examples, I speak both SAS and R.

Best Answer

You could do a grid search: start with ARIMA(1,0,0) and try all the possibilities up to ARIMA(5,2,5) or something. Fit the model to each series, and estimate a scale-independent error measurement like MAPE or MASE (MASE would probably be better). Choose the ARIMA model with the lowest average MASE across all your models.

You could improve this procedure by cross-validating your error measurement for each series, and also by comparing your results to a naive forecast.

It might be a good idea to ask why you're looking for a single model to describe all of the series. Unless they're generated by the same process, this doesn't seem like a good idea.

Related Solutions

Solved – SAS ARIMA: estimate without identify? or auto.arima in SAS

You are fortunate to ask this question onn this site because IrishStat has been automating ARIMA models for over 30 years (sorry to give away your age Dave). Also Rob Hyndman wrote the auto.arima procedure in R. I have a connection as I took my first time series course in a short course by Box and Tiao at Carnegie - Mellon University in 1974 (giving away my age now). Also when I was the Chief of Statistical Research at Risk Data Corporation (in the early 1990s) I hired Terry Woodfield who authored the ETS software at the SAS Institute just before we were able to draw him away. I am sure PROC ARIMA has gone through many changes but i am sure that if you make contact with Terry he could probably help you.

Personally the way I learned it from Box, Tiao and Pack ARIMA modeling is an iterative process that should be gone through manually in stages with the user making decisions at various stages. That is not to say that good results cannot be obtained by automated procedures. In fact I think that Dave Reilly (IrishStat) along with his son Tom have so much experience doing this that they will contend that they could produce a better model with their algorithm than I can do manually and they may be right. But my point is that for a time series specialist to take that approach takes away some of the steps that help him really get to understand the characteristics of thee seris very well.

One thing that always troubled me in the early years was that the Box-Jenkins methodology was revered a little too much. Estimation is by conditional least squares and so the normality of the residuals is important and often overlooked (a buried secret). In the late 1970s i work on the problem of outliers in time series and Darryl Downing and I published a paper on the topic in JASA in 1982.

Since then other like Doug Martin, George Tiao and Ruey Tsay have made much bigger contributions. IrishStat is aware of that literature and has incorporated their ideas in his software. That is why he emphasizes checking for level shifts and outliers before fixating on an ARIMA model. That aspect of his software makes it somewhat unique. It is different from auto.arima and SAS/ETS. So keep that in mind in your search for other automated procedures using SAS.

I hope you appreciate this as an answer even though it does not directly answer questions 1 or 2. I am sure you can find Terry Woodfield on the internet or go directly to the SAS Institute with your questions which are very specific to SAS and really require someone with intimate knowledge of the SAS algorithms. I don't think you will find anyone on this site who could give you better help.

Solved – Time series modeling with dynamic regressors in SAS vs R

While it is not built in, it is easy enough to do:

library(forecast)
fity <- auto.arima(y, xreg=x)
fitx <- auto.arima(x)
forecast(fity,h=10,xreg=forecast(fitx,h=10)$mean)

However, the prediction intervals obtained do not account for the variance in the forecasts of x. I doubt that SAS handles this either.

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Related Solutions

Solved – SAS ARIMA: estimate without identify? or auto.arima in SAS

Solved – Time series modeling with dynamic regressors in SAS vs R

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