# Inference for heavy tailed stationary time series based on sliding blocks

## TL;DR

This paper demonstrates that using sliding blocks in extreme value analysis of heavy-tailed stationary time series improves inference efficiency over disjoint blocks, with consistent variance reduction regardless of serial dependence.

## Contribution

It provides theoretical and empirical evidence that sliding blocks enhance the efficiency of extreme value inference for heavy-tailed time series, independent of serial dependence.

## Key findings

- Sliding blocks reduce asymptotic variance of estimators by over 18%.
- Efficiency gain is independent of serial dependence structure.
- Application to stock market data illustrates practical benefits.

## Abstract

The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, the maxima are taken over disjoint blocks of observations. Alternatively, the blocks can be chosen to slide through the observation period, yielding a larger number of overlapping blocks. Inference based on sliding blocks is found to be more efficient than inference based on disjoint blocks. The asymptotic variance of the maximum likelihood estimator of the Fr\'{e}chet shape parameter is reduced by more than 18%. Interestingly, the amount of the efficiency gain is the same whatever the serial dependence of the underlying time series: as for disjoint blocks, the asymptotic distribution depends on the serial dependence only through the sequence of scaling constants. The findings are illustrated by simulation experiments and are applied to the estimation of high return levels of the daily log-returns of the Standard & Poor's 500 stock market index.