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February 2021 Convergence of covariance and spectral density estimates for high-dimensional locally stationary processes
Danna Zhang, Wei Biao Wu
Ann. Statist. 49(1): 233-254 (February 2021). DOI: 10.1214/20-AOS1954

Abstract

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 nonstationary 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.

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Danna Zhang. Wei Biao Wu. "Convergence of covariance and spectral density estimates for high-dimensional locally stationary processes." Ann. Statist. 49 (1) 233 - 254, February 2021. https://doi.org/10.1214/20-AOS1954

Information

Received: 1 November 2018; Revised: 1 November 2019; Published: February 2021
First available in Project Euclid: 29 January 2021

Digital Object Identifier: 10.1214/20-AOS1954

Subjects:
Primary: 62M10
Secondary: 62M15

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 1 • February 2021
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