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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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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DOI: https://doi.org/10.1007/s10687-016-0258-0
Keywords
- Asymptotic independence
- Bayesian semiparametrics
- Conditional extremes
- Dirichlet process
- Extreme value theory
- Extremogram
- Risk analysis
- Threshold-based extremal index