GRADIENT-BASED STRUCTURAL CHANGE DETECTION FOR NONSTATIONARY TIME SERIES M-ESTIMATION

• 成果类型: Article
• 署名作者: Wu, Weichi; Zhou, Zhou
• 署名单位: University of London; University College London; University of Toronto
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1582
• 发表日期: 2018
• 页码: 1197-1224
• 关键词: varying-coefficient models; linear-models; REGRESSION QUANTILES; heteroscedasticity; REPRESENTATION; constancy; inference; tests

摘要

We consider structural change testing for a wide class of time series M-estimation with nonstationary predictors and errors. Flexible predictor-error relationships, including exogenous, state-heteroscedastic and autoregressive regressions and their mixtures, are allowed. New uniform Bahadur representations are established with nearly optimal approximation rates. A CUSUMtype test statistic based on the gradient vectors of the regression is considered. In this paper, a simple bootstrap method is proposed and is proved to be consistent for M-estimation structural change detection under both abrupt and smooth nonstationarity and temporal dependence. Our bootstrap procedure is shown to have certain asymptotically optimal properties in terms of accuracy and power. A public health time series dataset is used to illustrate our methodology, and asymmetry of structural changes in high and low quantiles is found.