# Temporal evolution of the extreme excursions of multivariate kth order Markov processes with application to oceanographic data

arXiv: https://arxiv.org/abs/2302.14501 · HTML: https://mlsanity.com/paper/2302.14501/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2023.

## Built on by (most cited first, 1 of 1)

- [Deep learning joint extremes of metocean variables using the SPAR model](https://mlsanity.com/paper/2412.15808/) (2024)

## Abstract (arXiv)

We develop two models for the temporal evolution of extreme events of multivariate kth 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.