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Banded and Tapered Estimates for Autocovariance Matrices and the Linear Process Bootstrap

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  • McMurry, Timothy L
  • Politis, D N
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    Abstract

    We address the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down-weighting o�-diagonal entries towards zero. In addition we show the same convergence rates hold for a positive de�nite version of the estimator, and we introduce a new approach for selecting the banding parameter. The new matrix estimator is shown to perform well theoretically and in simulation studies. As an application we introduce a new resampling scheme for stationary processes termed the linear process bootstrap (LPB). The LPB is shown to be asymptotically valid for the sample mean and related statistics. The e�ectiveness of the proposed methods are demonstrated in a simulation study.

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    Bibliographic Info

    Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt5h9259mb.

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    Date of creation: 31 Mar 2010
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    Handle: RePEc:cdl:ucsdec:qt5h9259mb

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    Keywords: autocovariance matrix; stationary process; boostrap; block bootstrap; sieve bootstrap; Social and Behavioral Sciences;

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    1. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
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