CONVERGENCE OF COVARIANCE AND SPECTRAL DENSITY ESTIMATES FOR HIGH-DIMENSIONAL LOCALLY STATIONARY PROCESSES

• 成果类型: Article
• 署名作者: Zhang, Danna; Wu, Wei Biao
• 署名单位: University of California System; University of California San Diego; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/20-AOS1954
• 发表日期: 2021
• 页码: 233-254
• 关键词: nonstationary time-series; quadratic-forms; Graphical Models; large deviations; tail probabilities; connectivity; coherence; brain; ARCH; identification

摘要

Covariances and spectral density functions play a fundamental role in the theory of time series. There is a well-developed asymptotic theory for their estimates for low-dimensional stationary processes. For high-dimensional non-stationary processes, however, many important problems on their asymptotic behaviors are still unanswered. This paper presents a systematic asymptotic theory for the estimates of time-varying second-order statistics for a general class of high-dimensional locally stationary processes. Using the framework of functional dependence measure, we derive convergence rates of the estimates which depend on the sample size T, the dimension p, the moment condition and the dependence of the underlying processes.