Bayesian uncertainty management in temporal dependence of extremes

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Authors Thomas Lugrin, Anthony C. Davison, Jonathan A. Tawn
Journal/Conference Name Extremes
Paper Category
Paper Abstract Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index 0 < 𝜃 ≤ 1 is a natural limiting measure of clustering, but for wide classes of dependent processes, including all stationary Gaussian processes, it cannot distinguish dependent processes from independent processes with 𝜃 = 1. Eastoe and Tawn (Biometrika 99, 43–55 2012) exploit methods from multivariate extremes to treat the subasymptotic extremal dependence structure of stationary time series, covering both 0 < 𝜃 < 1 and 𝜃 = 1, through the introduction of a threshold-based extremal index. Inference for their dependence models uses an inefficient stepwise procedure that has various weaknesses and has no reliable assessment of uncertainty. We overcome these issues using a Bayesian semiparametric approach. Simulations and the analysis of a UK daily river flow time series show that the new approach provides improved efficiency for estimating properties of functionals of clusters.
Date of publication 2015
Code Programming Language R

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