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Testing for equal predictive accuracy with strong dependence

Laura Coroneo () and Fabrizio Iacone ()

Discussion Papers from Department of Economics, University of York

Abstract: We revisit the Diebold and Mariano (1995) test, investigating the consequences of having autocorrelation in the loss differential. This situation can arise not only when a forecast is sub-optimal under MSE loss, but also when it is optimal under an alternative loss, or it is evaluated on a short sample, or when a forecast with weakly dependent forecast errors is compared to a naive benchmark. We show that the power of the Diebold and Mariano (1995) test decreases as the dependence increases, making it more difficult to obtain statistically significant evidence of superior predictive ability against less accurate benchmarks. Moreover, we find that after a certain threshold the test has no power and the correct null hypothesis is spuriously rejected. Taken together, these results caution to seriously consider the dependence properties of the selected forecast and of the loss differential before the application of the Diebold and Mariano (1995) test, especially when naive benchmarks are considered.

Keywords: strong autocorrelation; Forecast evaluation; Diebold and Mariano Test; Long Run Variance Estimation. (search for similar items in EconPapers)
JEL-codes: C12 C32 C53 (search for similar items in EconPapers)
Date: 2021-05
New Economics Papers: this item is included in nep-ecm and nep-ets
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