We investigate forecasting in models that condition on variables for which future values are unknown. We consider the role of the significance level because it guides the binary decisions whether to include or exclude variables. The analysis is extended by allowing for a structural break, either in the first forecast period or just before. Theoretical results are derived for a three-variable static model, but generalized to include dynamics and many more variables in the simulation experiment. The results show that the trade-off for selecting variables in forecasting models in a stationary world, namely that variables should be retained if their noncentralities exceed unity, still applies in settings with structural breaks. This provides support for model selection at looser than conventional settings, albeit with many additional features explaining the forecast performance, and with the caveat that retaining irrelevant variables that are subject to location shifts can worsen forecast performance.
Castle, J.L., Doornik, J.A. & Hendry, D.F. (2018). 'Selecting a Model for Forecasting'. Econometrics 9(3). https://doi.org/10.3390/econometrics9030026