Nonasymptotic bounds for autoregressive time series modeling

• 成果类型: Article
• 署名作者: Goldenshluger, A; Zeevi, A
• 署名单位: University of Haifa; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 417-444
• 关键词: asymptotically efficient selection; ORDER

摘要

The subject of this paper is autoregressive (AR) modeling of a stationary, Gaussian discrete time process, based on a finite sequence of observations. The process is assumed to admit an AR(co) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well the process can be approximated by a finite-order AR model. A lower bound on the accuracy of AR approximations is derived, and a nonasymptotic upper bound on the accuracy of the regularized least squares estimator is established. It is shown that with a proper choice of the model order, this estimator is minimax optimal in order. These considerations lead also to a nonasymptotic upper bound on the mean squared error of the associated one-step predictor, A numerical study compares the common model selection procedures to the minimax optimal order choice.