REVIEW 1 cited by
On the computation of the extremal index for time series
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
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 shows 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.
Forward citations
Cited by 1 Pith paper
-
Filtering and Statistical Properties of Unimodal Maps Perturbed by Heteroscedastic Noises
For a class of unimodal maps with state-dependent dynamical and observational noise, the paper proves filter stability, a central limit theorem, and large deviations; extreme value and Poisson results are proven only ...
Discussion (0). Continue with ORCID to comment.