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arXiv · 2302.14501

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

Stan Tendijck·Philip Jonathan·David Randell·Jonathan Tawn
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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.

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Stan Tendijck, Philip Jonathan, David Randell, Jonathan Tawn. 2023-02-28. Temporal evolution of the extreme excursions of multivariate $k$th order Markov processes with application to oceanographic data. https://arxiv.org/abs/2302.14501

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