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
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
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