## The Annals of Statistics

### Asymptotic spectral theory for nonlinear time series

#### 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

https://projecteuclid.org/euclid.aos/1188405630

Digital Object Identifier
doi:10.1214/009053606000001479

Mathematical Reviews number (MathSciNet)
MR2351105

Zentralblatt MATH identifier
1147.62076

#### 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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