Title: Gradient-based structural change detection for non-stationary time series M-estimation
Authors: Weichi Wu - University College London (United Kingdom) [presenting]
Zhou Zhou - University of Toronto (Canada)
Abstract: Structural change testing is considered for a wide class of time series M-estimation with non-stationary predictors and errors. Flexible predictor-error relationships, including exogenous, endogenous and autoregressive regressions and their mixtures, are allowed. New uniform Bahadur representations are established with nearly optimal approximation rates. A CUSUM-type test statistic based on the gradient vectors of the regression is considered. A simple bootstrap method is proposed and is proved to be consistent for M-estimation structural change detection under both abrupt and smooth non-stationarity 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 data set is used to illustrate our methodology, and asymmetry of structural changes in high and low quantiles are found.