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I've two questions regarding to the Diebold-Mariano test in comparing predictive acuraccy. I am reading this paper here.

Differences in MSPE are reported together with p-values from the Diebold– Mariano test (Newey–West adjusted), p.1505

  1. The authors "self-programmed" the Diebold-Mariano test with the regarding adjustment. Is this adjustment also done by Default in the dm.test function of the package forecast in R ? And why we have to adjust with this esimator ?

  2. It is common to use the two-sided version of the Diebold-Mariano test. What would be a appropriate reason to do a one-sided test in that case ?

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1 Answer 1

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  1. The HAC standard errors (e.g. Newey-West) are used to account for autocorrelation in the forecast errors/losses. They are present by design for multiple-step forecasts generated from consecutive rolling windows, as the forecast errors stem from overlapping time intervals. The forecast::dm.test function has this functionality, too.
  2. A one-sided test can be used if a priori there is no way that the expected value of the forecast loss differential is positive (negative). Usually, this is not realistic, as fancy forecasts do not always beat simple ones. (Also, if we look on the other sider, who could say for sure that a simple forecast will definitely beat a fancy one?)
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