Stan Tendijck | Searcharxiv

arXiv2023

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

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.

stat.ME↗

arXiv2022

Extremal Characteristics of Conditional Models

Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since the copula and marginals are not expressed in closed forms. We consider bivariate conditional models that specify the distribution of $X$ and the distribution of $Y$ conditional on $X$. We provide tools to quantify implicit assumptions on the extremes of this class of models. In particular, these tools allow us to approximate the distribution of the tail of $Y$ and the coefficient of asymptotic independence $η$ in closed forms. We apply these methods to a widely used conditional model for wave height and wave period. Moreover, we introduce a new condition on the parameter space for the conditional extremes model of Heffernan and Tawn (2004), and prove that the conditional extremes model does not capture $η$, when $η<1$.

math.ST↗