Predictive, finite-sample model choice for time series under stationarity and non-stationarity
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Date
2016
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Abstract
In statistical research there usually exists a choice between structurally simpler or
more complex models. We argue that, even if a more complex, locally stationary time
series model were true, then a simple, stationary time series model may be advantageous
to work with under parameter uncertainty. We present a new model choice
methodology, where one of two competing approaches is chosen based on its empirical
finite-sample performance with respect to prediction. A rigorous, theoretical analysis
of the procedure is provided. As an important side result we prove, for possibly diverging
model order, that the localised Yule-Walker estimator is strongly, uniformly
consistent under local stationarity. An R package, forecastSNSTS, is provided and
used to apply the methodology to financial and meteorological data in empirical examples.
We further provide an extensive simulation study and discuss when it is
preferable to base forecasts on the more volatile time-varying estimates and when it
is advantageous to forecast as if the data were from a stationary process, even though
they might not be.
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Keywords
forecasting, covariance stationarity, Yule-Walker estimate