Estimation of the extremal index using censored distributions

Extremes ◽  
2020 ◽  
Vol 23 (2) ◽  
pp. 197-213
Author(s):  
Jan Holešovský ◽  
Michal Fusek
Keyword(s):  
Extremal Index

scholarly journals Extreme value theory for piecewise contracting maps with randomly applied stochastic perturbations

2016 ◽  
Vol 16 (03) ◽  
pp. 1660015 ◽  
Author(s):  
Davide Faranda ◽  
Jorge Milhazes Freitas ◽  
Pierre Guiraud ◽  
Sandro Vaienti
Keyword(s):  
Extreme Value Theory ◽  
Stationary Process ◽  
Higher Dimensions ◽  
Value Theory ◽  
Extreme Value ◽  
Extremal Index ◽  
Limiting Distributions ◽  
Stochastic Perturbations

We consider globally invertible and piecewise contracting maps in higher dimensions and perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.

Extremes for shot noise processes with heavy tailed amplitudes

1997 ◽  
Vol 34 (03) ◽  
pp. 643-656 ◽  
Author(s):  
William P. McCormick
Keyword(s):  
Point Process ◽  
Shot Noise ◽  
Renewal Process ◽  
Poisson Point Process ◽  
Point Processes ◽  
Extremal Index ◽  
Two Dimensional ◽  
Limiting Behavior ◽  
Local Maxima ◽  
Heavy Tailed

Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where {τ k } are the points of a renewal process and {Ak } are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

scholarly journals Estimating the Extremal Index

1994 ◽  
Vol 56 (3) ◽  
pp. 515-528 ◽  
Author(s):  
Richard L. Smith ◽  
Ishay Weissman
Keyword(s):  
Extremal Index

scholarly journals Limiting crossing probabilities of random fields

2006 ◽  
Vol 43 (03) ◽  
pp. 884-891 ◽  
Author(s):  
L. Pereira ◽  
H. Ferreira
Keyword(s):  
General Theory ◽  
Long Range ◽  
Random Fields ◽  
Extremal Index ◽  
Weak Dependence ◽  
Local Path ◽  
Crossing Probabilities

Random fields on , with long-range weak dependence for each coordinate individually, usually present clustering of high values. For each one of the eight directions in , we formulate restriction conditions on local occurrence of two or more crossings of high levels. These smooth oscillation conditions enable computation of the extremal index as a clustering measure from the limiting mean number of crossings. In fact, only four directions must be inspected since for opposite directions we find the same local path crossing behaviour and the same limiting mean number of crossings. The general theory is illustrated with several 1-dependent nonstationary random fields.

scholarly journals Clustering of Extremes in Financial Returns: A Study of Developed and Emerging Markets

2020 ◽  
Vol 13 (7) ◽  
pp. 141
Author(s):  
Sara Ali Alokley ◽  
Mansour Saleh Albarrak
Keyword(s):  
Emerging Markets ◽  
Extremal Index ◽  
Threshold Values ◽  
Financial Returns ◽  
Dependency Structure ◽  
Developed Markets ◽  
Financial Events ◽  
Index Value ◽  
Shed Light ◽  
Interval Estimator

This paper investigates the clustering or dependency of extremes in financial returns by estimating the extremal index value, in which smaller values of the extremal index correspond to more clustering. We apply the interval estimator method to determine the extremal index for a range of threshold values in the developed and emerging markets from 2007–2017. The indices we used to represent developed markets are from France, Germany, Italy, Japan, USA, UK, Spain, and Sweden. For the emerging markets, we use indices from China, Brazil, India, Malaysia, Russia, Saudi Arabia, and Portugal. The results show that clustering occurs in the emerging and developed markets under several threshold values. This study will shed light on the dependency structure of financial returns data and the proprieties of the extremes returns. Moreover, understanding clustering of extremes in these markets can help investors reduce the exposure to extreme financial events, such as the financial crisis.

Sign in / Sign up

Export Citation Format

Share Document