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