The Annals of Statistics

Asymptotic spectral theory for nonlinear time series

Xiaofeng Shao and Wei Biao Wu

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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.

Article information

Ann. Statist., Volume 35, Number 4 (2007), 1773-1801.

First available in Project Euclid: 29 August 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M15: Spectral analysis 62E20: Asymptotic distribution theory
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

cumulants Fourier transform frequency domain bootstrap geometric moment contraction lag window estimator periodogram spectral density estimates


Shao, Xiaofeng; Wu, Wei Biao. Asymptotic spectral theory for nonlinear time series. Ann. Statist. 35 (2007), no. 4, 1773--1801. doi:10.1214/009053606000001479.

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