The Annals of Statistics

Nonparametric inference of quantile curves for nonstationary time series

Zhou Zhou

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 11 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.aos/1278861246

Digital Object Identifier
doi:10.1214/09-AOS769

Mathematical Reviews number (MathSciNet)
MR2676887

Zentralblatt MATH identifier
1202.62062

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

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

Citation

Zhou, Zhou. Nonparametric inference of quantile curves for nonstationary time series. Ann. Statist. 38 (2010), no. 4, 2187--2217. doi:10.1214/09-AOS769. https://projecteuclid.org/euclid.aos/1278861246


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