From Auto.arima to forecast in R

Question

I don't quite understand the syntax of how forecast() applies external regressors in the library(forecast) in R.

My fit looks like this:

fit <- auto.arima(Y,xreg=factors)

where Y is a timeSeries object 100 x 1 and factors is a timeSeries object 100 x 5.

When I go to forecast, I apply...

forecast(fit, h=horizon)

And I get an error:

Error in forecast.Arima(fit, h = horizon) : No regressors provided

Does it want me to add back the xregressors from the fit? I thought these were included in the fit object as fit$xreg. Does that mean it's asking for future values of the xregressors, or that I should repeat the same values I used in the fit set? The documentation doesn't cover the meaning of xreg in the forecast step.

I believe all this means I should use

forecast(fit, h=horizon,xreg=factors)

or

forecast(fit, h=horizon,xreg=fit$xreg)

Which gives the same results. But I'm not sure whether the forecast step is interpreting the factors as future values, or appropriately as previous ones. So,

1. Is this doing a forecast out of purely past values, as I expect?
2. Why do I have to specify the xreg values twice? It doesn't run if I exclude them, so it doesn't behave like an option.

Answer 1

Correct me if I am wrong, but I think you may not completely understand how the ARIMA model with regressors works.

When you forecast with a simple ARIMA model (without regressors), it simply uses past values of your time series to predict future values. In such a model, you could simply specify your horizon, and it would give you a forecast until that horizon.

When you use regressors to build an ARIMA model, you need to include future values of the regressors to forecast. For example, if you used temperature as a regressor, and you were predicting disease incidence, then you would need future values of temperature to predict disease incidence.

In fact, the documentation does talk about xreg specifically. look up ?forecast.Arima and look at both the arguments h and xreg. You will see that If xreg is used, then h is ignored. Why? Because if your function uses xreg, then it needs them for forecasting.

So, in your code, h was simply ignored when you included xreg. Since you just used the values that you used to fit the model, it just gave you all the predictions for the same set of regressors as if they were in the future.

Answer 2

related https://stats.stackexchange.com/questions/110589/arima-with-xreg-rebuilding-the-fitted-values-by-hand

I read that arima in R is borked See Issue 3 and 4

https://www.stat.pitt.edu/stoffer/tsa4/Rissues.htm

the xreg was suggested to derive the proper intercept.

I'm using real statistics for excel to figure out what is the actual constant. I had a professor tell me you need to have a constant

These derive the same forecasts. So it appears you can use xreg to get some descriptive information, but you would have to use the statsexchange link to manually derive from them.

f = auto.arima(lacondos[,1])

f$coef

g = Arima(lacondos[,1],c(t(matrix(arimaorder(f)))),include.constant=FALSE,xreg=1:length(lacondos[,1]))

g$coef