Structural Change Detection for Regression Quantiles Under Time Series Nonstationarity

• Activity Number: 419
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Weichi Wu* and Zhou Zhou
• Companies: and University of Toronto
• Keywords: Quantile regression ; piece-wise locally stationary ; bootstrap ; CUSUM ; structural change

Abstract

We consider quantile structural change testing for linear models with random designs and a wide class of non-stationary regressors and errors. New uniform Bahadur representations are established with nearly optimal approximation rates. Two cusum-type test statistics, one based on the regression coefficients and the other based on the gradient vectors are considered. Two of the most frequently used change point testing procedures, pivotalization and independent wild bootstrap, are shown to be inconsistent for non-stationary time series quantile regression. In this paper, simple bootstrap methods are proposed and are proved to be consistent for regression quantile structural change detection under both abrupt and smooth non-stationarity and temporal dependence. Our bootstrap procedures are shown to have certain asymptotically optimal properties in terms of accuracy and power. Our methodology is applied to the USA real GDP series, and asymmetry of structural changes in different quantiles are found.