Peaks over thresholds modelling with multivariate generalized Pareto distributions

Preprint, 2016

The multivariate generalized Pareto distribution arises as the limit of a suitably normalized vector conditioned upon at least one component of that vector being extreme. Statistical modelling using multivariate generalized Pareto distributions constitutes the multivariate analogue of peaks over thresholds modelling with the univariate generalized Pareto distribution. We introduce a construction device which allows us to develop a variety of new and existing parametric tail dependence models. A censored likelihood procedure is proposed to make inference on these models, together with a threshold selectionprocedure and several goodness-of-fit diagnostics. We illustrate our methods on two data applications, one concerning the financial risk stemming from the stock prices of four large banks in the United Kingdom, and one aiming at estimating the yearly probability of a rainfall which could cause a landslide in northern Sweden.