Nonparametric inference of quantile curves for nonstationary time series

TL;DR

This paper develops nonparametric methods for testing the shape of quantile curves in nonstationary time series, with applications to climate extremes and tropical cyclone wind speeds.

Contribution

It introduces new nonparametric tests and confidence bands for quantile curves in nonstationary processes, utilizing Bahadur representation and bootstrap techniques.

Findings

Detected an upward trend in high quantile cyclone wind speeds.

No trend found in mean maximum wind speed.

Method effectively captures trends in climate extremes.

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.