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Testing for equal predictive accuracy with strong dependence

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  • Laura Coroneo
  • Fabrizio Iacone

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.

Suggested Citation

  • Laura Coroneo & Fabrizio Iacone, 2021. "Testing for equal predictive accuracy with strong dependence," Discussion Papers 21/03, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:21/03
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    More about this item

    Keywords

    strong autocorrelation; Forecast evaluation; Diebold and Mariano Test; Long Run Variance Estimation.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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