The Annals of Statistics

Asymptotic spectral theory for nonlinear time series

Xiaofeng Shao and Wei Biao Wu

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 29 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1188405630

Digital Object Identifier
doi:10.1214/009053606000001479

Mathematical Reviews number (MathSciNet)
MR2351105

Zentralblatt MATH identifier
1147.62076

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

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

Citation

Shao, Xiaofeng; Wu, Wei Biao. Asymptotic spectral theory for nonlinear time series. Ann. Statist. 35 (2007), no. 4, 1773--1801. doi:10.1214/009053606000001479. https://projecteuclid.org/euclid.aos/1188405630


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