Order Determination in Nonlinear Time Series by Penalized Least-Squares

Abstract

The determination of the order of an autoregressive model is of central interest when using a nonparametric modeling approach. While theory for kernel estimates of the autoregression function is well developed, dimensionality issues may arise when the order of the process increases. In this respect, multivariate adaptive regression splines offer an alternative worth considering because of their ability to efficiently control both bias and model dimension. Here, we present a penalized least-squares approach to order selection using multivariate adaptive regression splines to approximate the unknown regression function. The performance of the method is investigated through numerical simulations of linear and nonlinear models of different orders. Results suggest that the proposed method has a high probability of correct order selection, provided the sample size is sufficiently large with respect to the true order of the series. An analysis of electroencephalogram data is presented as an illustration.

Keywords:

• Nonparametric autoregression; Order selection; Penalized least-squares; Nonlinear time series; Multivariate adaptive regression splines; EEG modeling

Acknowledgment

The authors thank Prof. Roland Jouvent for providing the EEG data.