How long should a block be?

TL;DR

This paper examines the impact of block length choices in the block maximum method for extreme value analysis, proposing diagnostics and methods to select appropriate block sizes for better approximation.

Contribution

It introduces likelihood-based approaches and graphical diagnostics to determine suitable block lengths, addressing a gap in existing methodology.

Findings

Longer blocks can reduce asymptotic efficiency if chosen improperly.

Proposed diagnostics help identify optimal block lengths.

Illustrated methods with wind, river, and rainfall data.

Abstract

The block maximum method, which is widely used in extreme value analysis, uses a generalized extreme value distribution to approximate that of the maximum of m observations. The quality of this approximation depends on the value of m and may be poor if m is too small. Surprisingly little attention has been paid to the choice of the block length, although a good choice is crucial to the success of the method. In this paper we assess the effect of taking excessively long blocks in terms of asymptotic relative efficiency, and propose likelihood-based approaches and graphical diagnostics to determine whether a proposed block length is suitable, allowing for potential rounding and left-censoring of observations. We investigate our ideas using simulation and illustrate them using wind speed, river flow and rainfall data.