Estimation and inference of time-varying auto-covariance under complex trend: A difference-based approach

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