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Bayesian uncertainty management in temporal dependence of extremes

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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.

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Authors and Affiliations

  1. EPFL-FSB-MATHAA-STAT, Ecole Polytechnique Fédérale de Lausanne, Station 8, 1015, Lausanne, Switzerland

    T. Lugrin & A. C. Davison

  2. Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, UK

    J. A. Tawn

Authors
  1. T. Lugrin
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  2. A. C. Davison
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  3. J. A. Tawn
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Correspondence to T. Lugrin.

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This research was partially supported by the Swiss National Science Foundation.

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Lugrin, T., Davison, A.C. & Tawn, J.A. Bayesian uncertainty management in temporal dependence of extremes. Extremes 19, 491–515 (2016). https://doi.org/10.1007/s10687-016-0258-0

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