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Non-asymptotic bounds for autoregressive time series modeling (1999).
| Content Provider | CiteSeerX |
|---|---|
| Author | Goldenshluger, Alexander Zeevi, Assaf |
| Abstract | 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(1) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well can the process be approximated by a finite order autoregressive model. A lower bound on the accuracy of AR approximations is derived, and a non-asymptotic 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 non-asymptotic 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. 1 Introduction The standard methods for estimating parameters of time series are based on the assumption that ... |
| File Format | |
| Publisher Date | 1999-01-01 |
| Access Restriction | Open |
| Subject Keyword | Non-asymptotic Bound Autoregressive Time Series Modeling Non-asymptotic Upper Bound Proper Choice Nonparametric Minimax Framework Finite Sequence Minimax Optimal Order Choice Numerical Study Step Predictor Standard Method Finite Order Autoregressive Model Common Model Selection Procedure Time Series Gaussian Discrete Time Process Model Order Ar Approximation Square Estimator |
| Content Type | Text |
| Resource Type | Article |
