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