Temporal evolution of the extreme excursions of multivariate $k$th order Markov processes with application to oceanographic data

TL;DR

This paper introduces two new models for analyzing the evolution of extreme events in multivariate Markov processes, specifically applied to oceanographic data, improving upon existing methods in predictive accuracy.

Contribution

The paper extends the conditional extremes model to multivariate processes and develops a model order selection procedure, demonstrating improved performance over traditional methods.

Findings

Models outperform historical matching methodology

Effective in meteorological-oceanographic data analysis

Applicable to multivariate extreme event prediction

Abstract

We develop two models for the temporal evolution of extreme events of multivariate $k$th order Markov processes. The foundation of our methodology lies in the conditional extremes model of Heffernan & Tawn (2004), and it naturally extends the work of Winter & Tawn (2016,2017) and Tendijck et al. (2019) to include multivariate random variables. We use cross-validation-type techniques to develop a model order selection procedure, and we test our models on two-dimensional meteorological-oceanographic data with directional covariates for a location in the northern North Sea. We conclude that the newly-developed models perform better than the widely used historical matching methodology for these data.