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

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

Authors

Emily J. Whitehouse



Abstract

In this paper, we show that when computing standard Diebold-Mariano-type tests for equal forecast accuracy and forecast encompassing, the long-run variance can frequently be negative when dealing with multi-step-ahead predictions in small, but empirically relevant, sample sizes. We subsequently consider a number of alternative approaches to dealing with this problem, including direct inference in the problem cases and 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 recently proposed Coroneo and Iacone (2016) test, which is based on a weighted periodogram long-run variance estimator, offers the best finite sample size and power performance.

Journal Article Type Article
Publication Date Nov 1, 2017
Journal International Journal of Forecasting
Print ISSN 0169-2070
Electronic ISSN 0169-2070
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 33
Issue 4
APA6 Citation Harvey, D. I., Leybourne, S. J., & Whitehouse, E. J. (2017). Forecast evaluation tests and negative long-run variance estimates in small samples. International Journal of Forecasting, 33(4), https://doi.org/10.1016/j.ijforecast.2017.05.001
DOI https://doi.org/10.1016/j.ijforecast.2017.05.001
Keywords Forecast evaluation; Long-run variance estimation; Simulation; Diebold-Mariano test; Forecasting
Publisher URL http://www.sciencedirect.com/science/article/pii/S0169207017300559
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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