Model Selection for Nonlinear Time Series

We investigate the finite-sample performance of model selection criteria for local linear regression by simulation. Similarly to linear regression, the penalization term depends on the number of parameters of the model. In the context of nonparametric regression, we use a suitable quantity to account for the Equivalent Number of Parameters as previously suggested in the literature. We consider the following criteria: Rice T, FPE, AIC, Corrected AIC and GCV. To make results comparable with other data-driven selection criteria we consider also Leave-Out CV. We show that the properties of the penalization schemes are very different for some linear and nonlinear models. Finally, we set up a goodness-of-fit test for linearity based on bootstrap methods. The test has correct size and very high power against the alternatives investigated. Application of the methods proposed to macroeconomic and financial time series shows that there is evidence of nonlinearity.