I know that the Diebold-Mariano test is simply testing whether two forecasts are likely to forecast with the same accuracy (null hypothesis) or not (reject the null) based on some loss function.
But if the null is rejected, how to infer which of the two forecasts is better? Using loss functions and compare? For example, choose the forecast with the lower error regarding the chosen loss function?
Best Answer
You can see which forecast is more accurate in a particular application by comparing the losses (e.g. MSE or MAE) due to the competing forecasts. As simple as that.
The Diebold-Mariano test goes further in that its statistic tells you how likely this result is to be due to chance (so that the forecasts would actually be equal in population).
If the test tells you the forecast loss is unlikely to be equal in population, then it makes sense to proceed with the forecast that has the lower loss.