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

2020/03/10 by Yan Cui, Michael Levine, Cui, Yan +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2003.05006

openalex publication_date 2020/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• At the edge of Donsker's Theorem: Asymptotics of multiscale scan statistics

Related

• Auto-Regressive Approximations to Non-stationary Time Series, with Inference and Applications
• Autocovariance Estimation in the Presence of Changepoints
• Detecting Gradual Changes in Locally Stationary Processes
• Simultaneous inference for monotone and smoothly time-varying functions under complex temporal dynamics
• Prediction in locally stationary time series