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August 2010 Nonparametric inference of quantile curves for nonstationary time series
Zhou Zhou
Ann. Statist. 38(4): 2187-2217 (August 2010). DOI: 10.1214/09-AOS769


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.


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Zhou Zhou. "Nonparametric inference of quantile curves for nonstationary time series." Ann. Statist. 38 (4) 2187 - 2217, August 2010.


Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1202.62062
MathSciNet: MR2676887
Digital Object Identifier: 10.1214/09-AOS769

Primary: 62G10
Secondary: 60F17

Keywords: Climate change , Gaussian approximation , integrated squared difference test , local stationarity , nonstationary nonlinear time series , Quantile estimation , simultaneous confidence band

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • August 2010
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