Max-Stability at Work (or Not): Estimating Return Levels for Daily Rainfall Data

Abstract

When we are dealing with meteorological data, usually one is interested in the analysis of maximal observations and records over time, since these entail negative consequences—risk events. Extreme Value Theory has proved to be a powerful and useful tool to describe situations that may have a significant impact in many application areas, where knowledge of the behavior of the tail of a distribution is of main interest. The classical Gnedenko theorem establishes that there are three type of possible limit max-stable distributions for maxima of blocks of independent and identically distributed (iid) observations. However, for the types of data to which extreme value models are commonly applied, temporal independence is usually an unrealistic assumption and one could ask about the appropriateness of max-stable models. Luckily, stationary and weekly dependent series follow the same distributional limit laws as those of independent series, although with parameters affected by dependence. For rainfall data, we will play with these results, analyzing max-stability at work for rare events estimation and the real impact of “neglecting” iid property.