Tests for forecast encompassing when forecasts depend on estimated regression parameters

This article presents analytical and simulation results on the properties of two tests for forecast encompassing, allowing throughout for dependence of the forecasts on estimated regression parameters. One test, which was intended for forecasts that do not depend on regression parameters, was developed by Harvey, Leybourne, and Newbold. This test works relatively well when the size of the sample of forecast errors is very small. A second test, which explicitly accounts for uncertainty about the regression parameters, otherwise is comparable or preferable.