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Abstract:
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We consider structural change testing for a wide class of time se- ries M-estimation with non-stationary 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 opti- mal approximation rates. A CUSUM-type test statistic based on the gradient vectors of the regression is considered. In this paper, a sim- ple 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 dataset is used to illustrate our methodology, and asymmetry of structural changes in high and low quantiles are found.
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