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August 2007 Asymptotic spectral theory for nonlinear time series
Xiaofeng Shao, Wei Biao Wu
Ann. Statist. 35(4): 1773-1801 (August 2007). DOI: 10.1214/009053606000001479


We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.


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Xiaofeng Shao. Wei Biao Wu. "Asymptotic spectral theory for nonlinear time series." Ann. Statist. 35 (4) 1773 - 1801, August 2007.


Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1147.62076
MathSciNet: MR2351105
Digital Object Identifier: 10.1214/009053606000001479

Primary: 62E20 , 62M15
Secondary: 62M10

Keywords: Cumulants , Fourier transform , frequency domain bootstrap , geometric moment contraction , lag window estimator , periodogram , spectral density estimates

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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