Selecting a nonlinear time series model using weighted tests of equal forecast accuracy

Nonlinear time series models have become fashionable tools to describe and forecast a variety of economic time series. A closer look at reported empirical studies, however, reveals that these models apparently fit well in-sample, but rarely show a substantial improvement in out-of-sample forecasts, at least over linear models. One of the many possible reasons for this finding is the use of inappropriate model selection criteria and forecast evaluation criteria. In this paper we therefore propose a novel criterion, which we believe does more justice to the very nature of nonlinear models. Simulations show that this criterion outperforms those criteria currently in use, in the sense that the true nonlinear model is more often found to perform better in out-of-sample forecasting than a benchmark linear model. An empirical illustration for US GDP emphasizes its relevance.