Order Choice in Nonlinear Autoregressive Models

Abstract

An extensive literature has been devoted to the problem of order choice in autoregressive models. Most of alternative methods to hypothesis tests are based on the minimization of the Akaike Information Criterion (AIC) or on some of its variants. These methods have the main drawback to have to assume a parametric form for the autoregression function. The aim of this paper is to present a nonparametric approach that allows to estimate the autoregression order without limiting ourself to any restrictive parametric class of processes. Our technique is in the same spirit as AIC criterion, in the sense that it is based on the minimization of some prediction error. Both theoretical and computational aspects of this method are discussed in this paper.

Keywords:

• AMS 1980 subject classification
• Primary 62F12
• secondary 62G05

Keywords:

• Autoregressive
• Cross-validation
• kernel estimate
• nonlinear model
• nonparametric prediction
• order choice
• prediction error