U-statistics of local sample moments under weak dependence

TL;DR

This paper investigates the asymptotic behavior of U-statistics derived from local sample moments in weakly dependent processes, establishing their normality for large samples and enabling higher-order moment change detection.

Contribution

It introduces a new asymptotic normality result for U-statistics based on local moments in weakly dependent data, applicable to change detection.

Findings

Established asymptotic normality of the U-statistics

Applicable to change point testing for higher moments

Handles non-overlapping block structures in dependent data

Abstract

In this paper, we study the asymptotic distribution of some U-statistics whose entries are functions of empirical moments computed from non-overlapping consecutive blocks of an underlying weakly dependent process. The length of these blocks converges to infinity, and thus we consider U-statistics of triangular arrays. We establish asymptotic normality of such U-statistics. The results can be used to construct tests for changes of higher order moments.