Identification of non-linear additive autoregressive models

• 成果类型: Article
• 署名作者: Huang, JHZ; Yang, LJ
• 署名单位: University of Pennsylvania; Michigan State University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1369-7412.2004.05500.x
• 发表日期: 2004
• 页码: 463-477
• 关键词: adaptive regression splines; time-series; nonparametric identification; order determination; polynomial splines; tensor-products; selection

摘要

We propose a lag selection method for non-linear additive autoregressive models that is based on spline estimation and the Bayes information criterion. The additive structure of the autoregression function is used to overcome the 'curse of dimensionality', whereas the spline estimators effectively take into account such a structure in estimation. A stepwise procedure is suggested to implement the method proposed. A comprehensive Monte Carlo study demonstrates good performance of the method proposed and a substantial computational advantage over existing local-polynomial-based methods. Consistency of the lag selection method based on the Bayes information criterion is established under the assumption that the observations are from a stochastic process that is strictly stationary and strongly mixing, which provides the first theoretical result of this kind for spline smoothing of weakly dependent data.