Abstract
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.
Highlights
There are many approaches to formulating models when the sole objective is forecasting, from the very parsimonious through to large systems
We focus on regression models that are linear in the parameters, and consider model selection that is controlled by the nominal significance level for statistical significance
These results show that even facing breaks, the well-known trade-off for selecting variables in forecasting models, namely that variables should be retained if their noncentralities exceed 1, still applies, resulting in much looser significance levels than typically used
Summary
There are many approaches to formulating models when the sole objective is forecasting, from the very parsimonious through to large systems. Clements and Hendry (2001) suggest that this lack of agreement is the result of intermittent distributional shifts that affect alternative formulations in different ways We address this puzzle by analysing the selection of models in the pursuit of optimal mean square forecast error (MSFE) in settings with structural breaks.. The results confirm that regressors should be retained for forecasting if their noncentralities exceed unity, regardless of whether or not there is a structural break, or of the forecasting device used These analytic results map to a selection significance level of 16% in the bivariate case, much looser than conventional significance levels used. Appendix A provides analytical calculations and Supplementary Tables are given in Appendix B
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