Model Selection for Nonlinear Time Series

• Activity Number: 243
• Type: Topic Contributed
• Date/Time: Tuesday, August 13, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): Sebastiano Manzan*+
• Affiliation(s): University of Amsterdam
• Keywords: local linear regression ; nonlinear time series ; bootstrap ; linearity test ; goodness-of-fit test

Abstract

We investigate by simulation the performance of various model selection criteria for local linear regression. 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: T, FPE, AIC, Corrected AIC,GCV and BIC. We show that the different penalization schemes lead to very different results for some linear and nonlinear time series models. We discuss also the use of the plots of the penalized RSS as a function of the bandwidth as a qualitative tool to investigate the presence of nonlinearities in the time series. Finally, we set up a bootstrap test for linearity based on the comparison of parametric and nonparametric RSS. We show that the size of the test depends crucially on the criteria used to select bandwidth and order. The test has very high power against the alternatives investigated.