Quantile Inference and Change Point Test under Time Series Non-stationarity

Recently, the non-stationary time series data attracts increased attention from researchers. The main goal of the thesis is to develop the methodologies for quantile inference and change point test under time series non-stationarity. The first part of the thesis considers the simultaneous or functional inference of time-varying quantile curves for a class of non-stationary and long memory time series. New uniform Bahadur representations and Gaussian approximation schemes are established for a wide class of non-stationary and long memory linear processes. Furthermore, an asymptotic distributional theory is developed for the maxima of a class of non-stationary long memory Gaussian processes. With the latter theoretical results, simultaneous confidence bands for the above mentioned quantile curves with asymptotically correct coverage probabilities are constructed. The second part of the thesis considers 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.

Department dc:contributor.department

Statistics

Year dc:date.issued

2015

Author dc:creator

• Wu, Weichi

Advisor dc:contributor.advisor

• Zhou, Zhou

• Change Point Test
• Long Memory
• Non-stationary Time Series
• Quantile Regression
• Simultaneous Confidence Band

Handle dc:identifier.uri

http://hdl.handle.net/1807/71394

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/71394