Forecast Encompassing and Model Evaluation

Abstract

Tests for parameter constancy and the ability to encompass rival models are important parts of model evaluation. It is shown that the recently proposed forecast-encompassing test statistics have implicit null hypotheses that combine hypotheses of parameter constancy and complete parametric encompassing. An additional attraction of these tests is that they are easily calculated even for large-scale econometric models. However, just as minimum MSE is a necessary, but not sufficient, condition for model congruence, so the requirement that one model forecast variance-encompass another is a necessary condition for the first model to have constant parameters and encompass the other model.