Forecasting – ARIMA and External Regressors in SAS and R

categorical dataforecastingrsasseasonality

So I remember reading somewhere that when we have external regressors, auto.arima cannot make correct predictions for the order of difference for either seasonality or the main time series itself (correct me if I'm wrong!)

Now, I'd like to know whether we'd need to difference the external regressors as well? Also, in the case of having external regressors (a few time series and a few dummies for seasonal patterns in those time series), can auto.arima even calculate the optimal MA and AR?

Also, I have weekly seasonality as well as quarterly and yearly seasonality; since I can't specify that many seasonalities in auto.arima, I'm inputting a lot of dummy variables for quarters and months; will that yield mathematically correct results?

Further, for those of you who have worked with SAS, when using the forecast procedure and estimating the input variables (the external regressors), does it automatically calculate the MA and AR for each external regressor?

Best Answer

auto.arima can select the order of differencing automatically, and make appropriate forecasts taking account of these differences. It can also include regressors via the xreg argument, and select the appropriate model order taking account of the regressors. If you include regressors, these will be differenced along with the response variable as part of the estimation. You do not have to difference them first. Please read http://otexts.com/fpp/9/1 on how it works.

When you refer to the "MA and AR for each external regressor", I assume you must be thinking of a transfer function model. This is not the model that is fitted using auto.arima. Please see http://robjhyndman.com/hyndsight/arimax/ for a discussion of the various models involving ARIMA like terms and regressors.

Related Solutions

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.

Solved – Exogeneous regressors in auto.arima and using them in forecast function in R

If you fit an arima model with external regressions, you MUST provide newxreg to the predictions function. This goes for arima, auto.arima, and Arima. You cannot provide external regressors to ets.

xreg should contain the exogenous variables for the training set, and newxreg should contain those variables for the prediction set. If the nexreg contains variables you do not know the future values of, you will either need to forecast these variables or exclude them from the model.

Best Answer

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

Solved – Exogeneous regressors in auto.arima and using them in forecast function in R

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