OPTIMAL DIFFERENCE-BASED VARIANCE ESTIMATORS IN TIME SERIES: A GENERAL FRAMEWORK

• 成果类型: Article
• 署名作者: Chan, Kin Wai
• 署名单位: Chinese University of Hong Kong
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/21-AOS2154
• 发表日期: 2022
• 页码: 1376-1400
• 关键词: change-point detection; confidence-interval; heteroskedasticity; bootstrap; shift; tests

摘要

Variance estimation is important for statistical inference. It becomes nontrivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or suboptimally handle these nuisance structures. This paper develops a general framework for the estimation of the long-run variance for time series with nonconstant means. The building blocks are difference statistics. The proposed class of estimators is general enough to cover many existing estimators. Necessary and sufficient conditions for consistency are investigated. The first asymptotically optimal estimator is derived. Our proposed estimator is theoretically proven to be invariant to arbitrary mean structures, which may include trends and a possibly divergent number of discontinuities.