Estimation of cluster functionals for regularly varying time series: sliding blocks estimators

@article{Cissokho2020EstimationOC,
  title={Estimation of cluster functionals for regularly varying time series: sliding blocks estimators},
  author={Youssouph Cissokho and Rafal Kulik},
  journal={arXiv: Statistics Theory},
  year={2020}
}
Cluster indices describe extremal behaviour of stationary time series. We consider their sliding blocks estimators. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions that can be easily verified for a large class of models. In particular, we show that in the Peak over Threshold framework, sliding and disjoint blocks estimators have the same limiting variance. 
Estimation of cluster functionals for regularly varying time series: Runs estimators
Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time series, we obtain
Large deviations of lp-blocks of regularly varying time series and applications to cluster inference
In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion
On the Disjoint and Sliding Block Maxima method for piecewise stationary time series
Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for
Tail measures and regular variation
A general framework for the study of regular variation (RV) is that of Polish star-shaped metric spaces, while recent developments in [1] have discussed RV with respect to a properly localised
Shift-invariant homogeneous classes of random fields
: Let k·k : R d → [0 , ∞ ) be a 1-homogeneous measurable map and let T = R l or T = Z l with d, l two positive integers. For a given R d -valued random field (rf) Z ( t ) , t ∈ T , which satisfies E {k
Cluster Random Fields and Random-Shift Representations
: This paper investigates random-shift representations of α -homogeneous shift-invariant classes of random fields (rf’s) K α [ Z ], which were introduced in [1]. Here Z ( t ) , t ∈ T is a

References

SHOWING 1-10 OF 50 REFERENCES
A sliding blocks estimator for the extremal index
In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed
Weak convergence of a pseudo maximum likelihood estimator for the extremal index
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a
Asymptotics for sliding blocks estimators of rare events
Drees and Rootzen (2010) have established limit theorems for a general class of empirical processes of statistics that are useful for the extreme value analysis of time series, but do not apply to
The cluster index of regularly varying sequences with applications to limit theory for functions of multivariate Markov chains
We introduce the cluster index of a multivariate stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums
Inference for heavy tailed stationary time series based on sliding blocks
The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, the maxima are taken over
Regularly varying multivariate time series
The extremogram: a correlogram for extreme events
We consider a strictly stationary sequence of random vectors whose finite-dimensional distributions are jointly regularly varying with some positive index. This class of processes includes among
Peak-over-threshold estimators for spectral tail processes: random vs deterministic thresholds
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees et al. (Extremes 18 (3), 369–402, 2015 ) proposed estimators of the
...
...