A Generative High Quantile Homogeneity Test Using Bahadur Representation for Heteroskedastic High Quantile Regression of Tail Dependent Time Series

TL;DR

This paper introduces a novel high quantile homogeneity test for tail-dependent time series, leveraging Bahadur representation to handle heteroskedasticity and non-stationarity in high quantile regression.

Contribution

It develops a new Bahadur representation for tail-dependent time series, enabling the creation of a generative high quantile homogeneity test applicable under heteroskedasticity.

Findings

The test effectively detects heterogeneity in high quantiles.

Application to synthetic and real data demonstrates practical utility.

The Bahadur representation offers explicit error bounds for nonlinear estimators.

Abstract

We consider a high quantile homogeneity test to determine whether a certain set of explanatory variables has homogeneous effects on different high quantiles of the response variable in the tail. To accommodate for situations under both the null and the alternative, the auxiliary process in this case may no longer be treated as stationary, and the problem requires a joint analysis of both homoscedastic and heteroskedastic high quantiles. For this, we develop a novel Bahadur representation result in the high quantile setting for a general class of tail dependent time series under potential heteroskedasticity, which can be of interest by its own. In particular, the Bahadur representation provides a foundation for reducing problems regarding nonlinear high quantile regression estimators to those regarding suitably constructed linear forms with an explicit error bound and can be transformative and useful in many statistical problems. We in the current article apply it to guide the development of a generative high quantile homogeneity test, which is then illustrated through applications to both synthetic and real data.