Annals of Statistics

Nonparametric inference of quantile curves for nonstationary time series

Zhou Zhou

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The paper considers nonparametric specification tests of quantile curves for a general class of nonstationary processes. Using Bahadur representation and Gaussian approximation results for nonstationary time series, simultaneous confidence bands and integrated squared difference tests are proposed to test various parametric forms of the quantile curves with asymptotically correct type I error rates. A wild bootstrap procedure is implemented to alleviate the problem of slow convergence of the asymptotic results. In particular, our results can be used to test the trends of extremes of climate variables, an important problem in understanding climate change. Our methodology is applied to the analysis of the maximum speed of tropical cyclone winds. It was found that an inhomogeneous upward trend for cyclone wind speeds is pronounced at high quantile values. However, there is no trend in the mean lifetime-maximum wind speed. This example shows the effectiveness of the quantile regression technique.

Article information

Ann. Statist., Volume 38, Number 4 (2010), 2187-2217.

First available in Project Euclid: 11 July 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing
Secondary: 60F17: Functional limit theorems; invariance principles

Simultaneous confidence band integrated squared difference test quantile estimation nonstationary nonlinear time series local stationarity Gaussian approximation climate change


Zhou, Zhou. Nonparametric inference of quantile curves for nonstationary time series. Ann. Statist. 38 (2010), no. 4, 2187--2217. doi:10.1214/09-AOS769.

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