Information criteria for nonlinear time series models

In this paper the performance of different information criteria for simultaneous model class and lag order selection is evaluated using simulation studies. We focus on the ability of the criteria to distinguish linear and nonlinear models. In the simulation studies, we consider three different versions of the commonly known criteria AIC, SIC and AICc. In addition, we also assess the performance of WIC and evaluate the impact of the error term variance estimator. Our results confirm the findings of different authors that AIC and AICc favor nonlinear over linear models, whereas weighted versions of WIC and all versions of SIC are able to successfully distinguish linear and nonlinear models. However, the discrimination between different nonlinear model classes is more difficult. Nevertheless, the lag order selection is reliable. In general, information criteria involving the unbiased error term variance estimator overfit less and should be preferred to using the usual ML estimator of the error term variance.