Assaf Zeevi

Nonasymptotic bounds for autoregressive time series modeling

Coauthor(s): Alexander Goldenshluger.


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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(∞) 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.

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Source: Annals of Statistics
Exact Citation:
Goldenshluger, Alexander, and Assaf Zeevi. "Nonasymptotic bounds for autoregressive time series modeling." Annals of Statistics 29, no. 2 (April 2001): 417-444.
Volume: 29
Number: 2
Pages: 417-444
Date: 4 2001