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

12 Pages Posted: 12 Oct 2010

See all articles by Timothy L. McMurry

Timothy L. McMurry

DePaul University

Dimitris N. Politis

University of California, San Diego (UCSD) - Department of Mathematics

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 off-diagonal entries towards zero. In addition, we show the same convergence rates hold for a positive definite 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 effectiveness of the proposed methods are demonstrated in a simulation study.

Suggested Citation

McMurry, Timothy L. and Politis, Dimitris, Banded and Tapered Estimates for Autocovariance Matrices and the Linear Process Bootstrap. Journal of Time Series Analysis, Vol. 31, Issue 6, pp. 471-482, November 2010, Available at SSRN: https://ssrn.com/abstract=1688657 or http://dx.doi.org/10.1111/j.1467-9892.2010.00679.x

Timothy L. McMurry (Contact Author)

DePaul University ( email )

1 East Jackson Blvd.
Chicago, IL 60604
United States

Dimitris Politis

University of California, San Diego (UCSD) - Department of Mathematics ( email )

9500 Gilman Drive
La Jolla, CA 92093-0112
United States
858-534-5861 (Phone)
858-534-5273 (Fax)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
2
Abstract Views
305
PlumX Metrics