Including regressors to improve forecasts on white noise

Question

I am conducting some time series forecasts using quite limited data, 13 years annually. Basically, I am trying to forecast companies emission totals using historical values. The historical data however, seems to be nothing but white noise, e.g no significant lags on ACF, however Box Ljung <0.05.

My question is if it would be helpful to include correlated variables in a ARIMA model, with xreg..? For example including GDP, World Emissions, and Energy Prices. Would this improve the forecasts at all, or would any improvement on the test accuracy only be coincidences (limited data).

Answer 1

13 data points is extremely little. There is a very rough rule of thumb that you need 20 data points per parameter to be estimated, so you just have enough for an intercept term. Also, you really don't have enough data to do holdout testing - if you hold out, say, the last three data points, then you only have ten points to fit your model to, and how much would you want to rely on a holdout set of just three points?

By all means, try including regressors you believe might drive your time series. (Remember that you need to forecast future values of your regressors, too - this adds additional uncertainty!) Per above, I would not expect this to be very helpful.

Best method for short time-series may be useful.