Tests for forecast encompassing

We consider the situation in which two forecasts of the same variable are available. The possibility exists of forming a combined forecast as a weighted average of the individual ones and estimating the weights that should be optimally attached to each forecast. If the entire weight should optimally be associated with one forecast, that forecast is said to encompass the other. A natural test for forecast encompassing is based on least squares regression. We find, however, that the null distribution of this test statistic is not robust to nonnormality in the forecast errors. We discuss several alternative tests that are robust.