Model Selection for Non-Linear Dynamic Models

This paper develops tests for selection of competing non-linear dynamic models. The null hypothesis is that the models are equally close the Data Generating Process (DGP), according to a certain measure of closeness. The alternative is that one model is closer to the DGP. The models can be non-nested, overlapping, or nested. They can be correctly specified or not. Their parameters can be estimated by a variety of methods, including Maximum Likelihood, Non-Linear Least Squares, Method of Moments, where the choice depends on the selected measure of closeness to the DGP. The tests are symmetric and directional. Their asymptotic distribution under the null is either normal or a weighted sum of chi-square distributions, depending on the nesting characteristics of the competing models. The comparison of ARMAX and STAR models, and of nested ARMAX-GARCH models are discussed as examples.