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Banded and tapered estimates for autocovariance matrices and the linear process bootstrap
Author(s) -
McMurry Timothy L.,
Politis Dimitris N.
Publication year - 2010
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2010.00679.x
Subject(s) - autocovariance , mathematics , estimator , diagonal , convergence (economics) , weighting , resampling , matrix (chemical analysis) , statistics , range (aeronautics) , sample mean and sample covariance , mathematical optimization , algorithm , mathematical analysis , medicine , materials science , geometry , fourier transform , economics , composite material , radiology , economic growth
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.