Asymptotic spectral theory for nonlinear time series

Xiaofeng Shao, Biao Wu Wei

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)1773-1801
Number of pages29
JournalAnnals of Statistics
Issue number4
StatePublished - Aug 2007


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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