Selecting the variables in a time series (TS) regression model (ARDL model) for forecasting

[newsagent]

I have a (monthly) dependent macroeconomic variable y_t (deposits) and one independent variable x_t (GDP), plus some seasonal dummies.

The goal is forecasting.

I am trying various time series regression models that contain lags of y_t and x_t. So the models under investigation are ARDL(p,q) models.

Based on your excellent textbook for forecasting (7.5 section) that explains how to select the regressors:

A) I include or drop the regressors from my model based on whether they increase its forecasting accuracy.
B) I keep those variables that increase the forecasting performance of the model, even if they are statistically significant but have the wrong sign.
C) I drop the seasonal dummies if they decrease the forecast accucary of the model.
D) Of course, an alternative to the ARDL is the static TS regression model with ARIMA errors, which I could use.

Are my conclusions correct?

[newsagent]

Many thanks. So in this case, there is no need to use information criteria (IC) like AIC or BIC but only, say, the RMSEs. But why in section 7.5 you mention these IC regarding their usefulness in selecting the regressors?

[robjhyndman]

You did not mention how you were selecting predictors in your question. You can use information criteria, you can use test-set RMSEs, or various other methods. Information criteria are particularly useful as they use all the available data.

[newsagent]

Perfect!