Statistical models for dynamics in extreme value processes

TL;DR

This paper compares four statistical models for capturing the dynamics of extreme value processes, evaluating their fit to data and dependence structures through simulation and copula analysis.

Contribution

It introduces and assesses four different approaches to model time-dependent extremal behavior, providing insights into their effectiveness and differences.

Findings

Models capture different dependence structures

Copula plots reveal model fit to inter-arrival times

Simulation demonstrates model capabilities in extremal dynamics

Abstract

We study four different approaches to model time-dependent extremal behavior: dynamics introduced by (a) a state-space model (SSM), (b) a shot-noise-type process with GPD marginals, (c) a copula-based autoregressive model with GPD marginals, and (d) a GLM with GPD marginals (and previous extremal events as regressors). Each of the models is fit against data, and from the fitted data, we simulate corresponding paths according to the respective fitted models. At this simulated data, the respective dependence structure is analyzed in copula plots and judged against its capacity to fit the corresponding inter-arrival distribution.