Asymptotic spectral theory for nonlinear time series

Xiaofeng Shao; Biao Wu Wei

doi:10.1214/009053606000001479

Asymptotic spectral theory for nonlinear time series

Xiaofeng Shao
, Biao Wu Wei

Research output: Contribution to journal › Article › peer-review

123 Scopus citations

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.

Original language	English
Pages (from-to)	1773-1801
Number of pages	29
Journal	Annals of Statistics
Volume	35
Issue number	4
DOIs	https://doi.org/10.1214/009053606000001479
State	Published - Aug 2007

Keywords

Cumulants
Fourier transform
Frequency domain bootstrap
Geometric moment contraction
Lag window estimator
Periodogram
Spectral density estimates

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10.1214/009053606000001479

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title = "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.",

keywords = "Cumulants, Fourier transform, Frequency domain bootstrap, Geometric moment contraction, Lag window estimator, Periodogram, Spectral density estimates",

author = "Xiaofeng Shao and Wei, \{Biao Wu\}",

year = "2007",

month = aug,

doi = "10.1214/009053606000001479",

language = "English",

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pages = "1773--1801",

journal = "Annals of Statistics",

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T1 - Asymptotic spectral theory for nonlinear time series

AU - Shao, Xiaofeng

AU - Wei, Biao Wu

PY - 2007/8

Y1 - 2007/8

N2 - 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.

AB - 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.

KW - Cumulants

KW - Fourier transform

KW - Frequency domain bootstrap

KW - Geometric moment contraction

KW - Lag window estimator

KW - Periodogram

KW - Spectral density estimates

UR - https://www.scopus.com/pages/publications/34547953670

U2 - 10.1214/009053606000001479

DO - 10.1214/009053606000001479

M3 - Article

AN - SCOPUS:34547953670

SN - 0090-5364

VL - 35

SP - 1773

EP - 1801

JO - Annals of Statistics

JF - Annals of Statistics

IS - 4

ER -

Asymptotic spectral theory for nonlinear time series

Abstract

Keywords

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