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Bayesian uncertainty management in temporal dependence of extremes

Research output: Contribution to journalJournal article

<mark>Journal publication date</mark>09/2016
Issue number3
Number of pages25
Pages (from-to)491-515
Early online date4/06/16
<mark>Original language</mark>English


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 < ≤ 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 = 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 < <1 and = 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.

Bibliographic note

The final publication is available at Springer via http://dx.doi.org/10.1007/s10687-016-0258-0