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Nonparametric inference of quantile curves for nonstationary time series. (English) Zbl 1202.62062
Summary: 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.

MSC:
62G10 Nonparametric hypothesis testing
62M07 Non-Markovian processes: hypothesis testing
62P12 Applications of statistics to environmental and related topics
60F17 Functional limit theorems; invariance principles
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09 Nonparametric statistical resampling methods
62G15 Nonparametric tolerance and confidence regions
62G20 Asymptotic properties of nonparametric inference
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