Local linear quantile estimation for nonstationary time series

TL;DR

This paper develops methods for estimating quantile curves in nonstationary time series, providing theoretical guarantees and applying them to environmental data to assess climate variability changes.

Contribution

It introduces local linear quantile estimation techniques with consistency and CLT results for nonstationary processes, addressing a key gap in statistical methodology.

Findings

Consistent estimation of quantile curves under short-range dependence.

Application to climate data reveals potential changes in climate variability.

Provides a statistical framework for environmental time series analysis.

Abstract

We consider estimation of quantile curves for a general class of nonstationary processes. Consistency and central limit results are obtained for local linear quantile estimates under a mild short-range dependence condition. Our results are applied to environmental data sets. In particular, our results can be used to address the problem of whether climate variability has changed, an important problem raised by IPCC (Intergovernmental Panel on Climate Change) in 2001.