In statistical research there usually exists a choice between structurally simpler ormore complex models. We argue that, even if a more complex, locally stationary timeseries model were true, then a simple, stationary time series model may be advantageousto work with under parameter uncertainty. We present a new model choicemethodology, where one of two competing approaches is chosen based on its empiricalfinite-sample performance with respect to prediction. A rigorous, theoretical analysisof the procedure is provided. As an important side result we prove, for possibly divergingmodel order, that the localised Yule-Walker estimator is strongly, uniformlyconsistent under local stationarity. An R package, forecastSNSTS, is provided andused to apply the methodology to financial and meteorological data in empirical examples.We further provide an extensive simulation study and discuss when it ispreferable to base forecasts on the more volatile time-varying estimates and when itis advantageous to forecast as if the data were from a stationary process, even thoughthey might not be.
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