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

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

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.

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

• Journal Article Type: Article
• Acceptance Date: May 3, 2017
• Online Publication Date: Jun 15, 2017
• Publication Date: Nov 1, 2017
• Deposit Date: May 23, 2017
• Publicly Available Date: Jun 16, 2019
• Journal: International Journal of Forecasting
• Print ISSN: 0169-2070
• Electronic ISSN: 0169-2070
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 4
• DOI: https://doi.org/10.1016/j.ijforecast.2017.05.001
• Keywords: Forecast evaluation; Long-run variance estimation; Simulation; Diebold-Mariano test; Forecasting
• Public URL: https://nottingham-repository.worktribe.com/output/892023
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0169207017300559