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2021 Estimation and inference of time-varying auto-covariance under complex trend: A difference-based approach
Yan Cui, Michael Levine, Zhou Zhou
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Electron. J. Statist. 15(2): 4264-4294 (2021). DOI: 10.1214/21-EJS1893

Abstract

We propose a difference-based nonparametric methodology for the estimation and inference of the time-varying auto-covariance functions of a locally stationary time series when it is contaminated by a complex trend with both abrupt and smooth changes. Simultaneous confidence bands (SCB) with asymptotically correct coverage probabilities are constructed for the auto-covariance functions under complex trend. A simulation-assisted bootstrapping method is proposed for the practical construction of the SCB. Detailed simulation and a real data example round out our presentation.

Funding Statement

Zhou Zhou’s research has been partially supported by NSERC grant 489079.

Citation

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Yan Cui. Michael Levine. Zhou Zhou. "Estimation and inference of time-varying auto-covariance under complex trend: A difference-based approach." Electron. J. Statist. 15 (2) 4264 - 4294, 2021. https://doi.org/10.1214/21-EJS1893

Information

Received: 1 July 2020; Published: 2021
First available in Project Euclid: 14 September 2021

Digital Object Identifier: 10.1214/21-EJS1893

Keywords: Change points , Gaussian approximation , local stationarity , simultaneous confidence bands

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Vol.15 • No. 2 • 2021
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