Estimation and Inference of Time-Varying Auto-Covariance under Complex Trend: A Difference-based Approach

TL;DR

This paper introduces a difference-based nonparametric method for estimating and inferring time-varying auto-covariance functions in locally stationary time series affected by complex trends, with practical confidence bands and bootstrap techniques.

Contribution

It develops a novel difference-based approach for auto-covariance estimation under complex trends and provides asymptotically correct confidence bands with a bootstrap method.

Findings

Successful construction of simultaneous confidence bands with correct coverage.

Effective bootstrap method for practical implementation.

Demonstrated performance through simulations and real data analysis.

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.