Limit theorems for non-degenerate U-statistics of block maxima for time series

TL;DR

This paper develops limit theorems for non-degenerate U-statistics of block maxima in time series, improving estimators by using sliding blocks and extending results to multivariate and piecewise stationary cases.

Contribution

It introduces new asymptotic results for U-statistics of block maxima, including sliding blocks and multivariate extensions, with practical applications and simulations.

Findings

Sliding block maxima improve estimator efficiency.

Limit theorems hold for multivariate and piecewise stationary series.

Monte Carlo simulations demonstrate finite-sample performance.

Abstract

The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding rather than disjoint block maxima. Similar results are derived for general non-degenerate U-statistics of arbitrary order, in the multivariate time series case. Details are worked out for selected examples: the empirical variance, the probability weighted moment estimator and Kendall's tau statistic. The results are also extended to the case where the underlying sample is piecewise stationary. The finite-sample properties are illustrated by a Monte Carlo simulation study.