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

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  • David I. Harvey
  • Stephen J. Leybourne
  • 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.

Suggested Citation

  • David I. Harvey & Stephen J. Leybourne & Emily J. Whitehouse, 2017. "Forecast evaluation tests and negative long-run variance estimates in small samples," Discussion Papers 17/03, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:17/03
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    7. Wang, Lu & Ma, Feng & Liu, Jing & Yang, Lin, 2020. "Forecasting stock price volatility: New evidence from the GARCH-MIDAS model," International Journal of Forecasting, Elsevier, vol. 36(2), pages 684-694.
    8. Zhou, Jin & Li, Haiqi & Zhong, Wanling, 2021. "A modified Diebold–Mariano test for equal forecast accuracy with clustered dependence," Economics Letters, Elsevier, vol. 207(C).
    9. Håvard Hungnes, 2020. "Equal predictability test for multi-step-ahead system forecasts invariant to linear transformations," Discussion Papers 931, Statistics Norway, Research Department.
    10. Yang, Kailing & Zhang, Xi & Luo, Haojia & Hou, Xianping & Lin, Yu & Wu, Jingyu & Yu, Liang, 2024. "Predicting energy prices based on a novel hybrid machine learning: Comprehensive study of multi-step price forecasting," Energy, Elsevier, vol. 298(C).
    11. Dimitriadis, Timo & Liu, Xiaochun & Schnaitmann, Julie, 2020. "Encompassing tests for value at risk and expected shortfall multi-step forecasts based on inference on the boundary," Hohenheim Discussion Papers in Business, Economics and Social Sciences 11-2020, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    12. Rubaszek Michal & Karolak Zuzanna & Kwas Marek & Uddin Gazi Salah, 2020. "The role of the threshold effect for the dynamics of futures and spot prices of energy commodities," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(5), pages 1-20, December.
    13. Schlösser, Alexander, 2020. "Forecasting industrial production in Germany: The predictive power of leading indicators," Ruhr Economic Papers 838, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    14. Hwee Kwan Chow & Yijie Fei & Daniel Han, 2023. "Forecasting GDP with many predictors in a small open economy: forecast or information pooling?," Empirical Economics, Springer, vol. 65(2), pages 805-829, August.
    15. Costantini, Mauro & Kunst, Robert M., 2021. "On using predictive-ability tests in the selection of time-series prediction models: A Monte Carlo evaluation," International Journal of Forecasting, Elsevier, vol. 37(2), pages 445-460.
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    18. Qin Lu & Jingwen Liao & Kechi Chen & Yanhui Liang & Yu Lin, 2024. "Predicting Natural Gas Prices Based on a Novel Hybrid Model with Variational Mode Decomposition," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 639-678, February.

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    Keywords

    Forecast evaluation; Long-run variance estimation; Simulation; Diebold-Mariano test; Forecasting;
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