A necessary and sufficient condition for asymptotic independence of discrete Fourier transforms under short- and long-range dependence

• 成果类型: Article
• 署名作者: Lahiri, SN
• 署名单位: Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1051027883
• 发表日期: 2003
• 页码: 613-641
• 关键词: LOG-PERIODOGRAM REGRESSION; time-series; normality

摘要

Let {X-t} be a stationary time series and let d(T) (lambda) denote the discrete Fourier transform (DFT) of {X-0,...,XT-1} with a data taper. The main results of this paper provide a characterization of asymptotic independence of the DFTs in terms of the distance between their arguments under both short- and long-range dependence of the process (Xt). Further, asymptotic joint distributions of the DFTs d(T) (lambda(1T)) and d(T) (lambda(2T)) are also established for the cases T(lambda(1T) - lambda(2T)) = O(1) as T --> infinity (asymptotically close ordinates) and \T(lambda(1T) - lambda(2T))\ --> infinity as T --> infinity (asymptotically distant ordinates). Some implications of the main results on the estimation of the index of dependence are also discussed.