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Article Dans Une Revue Journal of Statistical Physics Année : 2020

On the Computation of the Extremal Index for Time Series

Résumé

The extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances. In the dynamical systems framework, it provides important information about the dynamics of the underlying systems. In this paper we provide a review of the meaning of the extremal index in dynamical systems. Depending on the observables used, this quantity can inform on local properties of attractors such as periodicity, stability and persistence in phase space, or on global properties such as the Lyapunov exponents. We also introduce a new estimator of the extremal index and show its relation with those previously introduced in the statistical literature. We reserve a particular focus to the systems perturbed with noise as they are a good paradigm of many natural phenomena. Different kind of noises are investigated in the annealed and quenched situations. Applications to climate data are also presented.
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Dates et versions

hal-02450472 , version 1 (09-02-2020)

Identifiants

Citer

Th Caby, D. Faranda, Sandro Vaienti, Pascal Yiou. On the Computation of the Extremal Index for Time Series. Journal of Statistical Physics, 2020, 179 (5-6), pp.1666-1697. ⟨10.1007/s10955-019-02423-z⟩. ⟨hal-02450472⟩
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