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

Lookup NU author(s): Dr Emily WhitehouseORCiD

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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.

Publication metadata

Author(s): Harvey DI, Leybourne SJ, Whitehouse EJ

Publication type: Article

Publication status: Published

Journal: International Journal of Forecasting

Year: 2017

Volume: 33

Issue: 4

Pages: 833-847

Print publication date: 01/10/2017

Online publication date: 15/06/2017

Acceptance date: 03/05/2017

Date deposited: 05/07/2018

ISSN (print): 0169-2070

Publisher: Elsevier

URL: https://doi.org/10.1016/j.ijforecast.2017.05.001

DOI: 10.1016/j.ijforecast.2017.05.001

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