Asymptotic spectral theory for nonlinear time series

• 成果类型: Article
• 署名作者: Shao, Xiaofeng; Wu, Wei Biao
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001479
• 发表日期: 2007
• 页码: 1773-1801
• 关键词: iterated random functions; AUTOREGRESSIVE PROCESSES; Empirical distribution; fourier coefficients; stationary process; garch processes; LIMIT-THEOREMS; markov-chains; Periodogram; models

摘要

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodograrn 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.