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Forecast evaluation tests and negative long-run variance estimates in small samples

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  • Harvey, David I.
  • Leybourne, Stephen J.
  • Whitehouse, Emily J.

Abstract

This paper shows that the long-run variance can frequently be negative when computing standard Diebold–Mariano-type tests for equal forecast accuracy and forecast encompassing if one is dealing with multi-step-ahead predictions in small, but empirically relevant, sample sizes. We therefore consider a number of alternative approaches for dealing with this problem, including direct inference in the problem cases and the use of long-run variance estimators that guarantee positivity. The finite sample size and power of the different approaches are evaluated using extensive Monte Carlo simulation exercises. Overall, for multi-step-ahead forecasts, we find that the test recently proposed by Coroneo and Iacone (2016), which is based on a weighted periodogram long-run variance estimator, offers the best finite sample size and power performance.

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  • Harvey, David I. & Leybourne, Stephen J. & Whitehouse, Emily J., 2017. "Forecast evaluation tests and negative long-run variance estimates in small samples," International Journal of Forecasting, Elsevier, vol. 33(4), pages 833-847.
    • Handle: RePEc:eee:intfor:v:33:y:2017:i:4:p:833-847
    DOI: 10.1016/j.ijforecast.2017.05.001
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