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Predictive, finite-sample model choice for time series under stationarity and non-stationarity

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  • Kley, Tobias
  • Preuss, Philip
  • Fryzlewicz, Piotr

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, in a manner that ensures interpretability. 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.

Suggested Citation

  • Kley, Tobias & Preuss, Philip & Fryzlewicz, Piotr, 2019. "Predictive, finite-sample model choice for time series under stationarity and non-stationarity," LSE Research Online Documents on Economics 101748, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:101748
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    File URL: http://eprints.lse.ac.uk/101748/
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    Cited by:

    1. Sourav Das & Suhasini Subba Rao & Junho Yang, 2021. "Spectral methods for small sample time series: A complete periodogram approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 597-621, September.
    2. Holger Dette & Weichi Wu, 2020. "Prediction in locally stationary time series," Papers 2001.00419, arXiv.org, revised Jan 2020.

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    More about this item

    Keywords

    forecasting; Yule-Walker estimate; local stationarity; covariance stationarity; EP/L014246/1;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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