Extreme value theory for multivariate stationary sequences

DOI10.1016/0047-259X(89)90028-6zbMath0679.62039MaRDI QIDQ1822865

Tailen Hsing

Publication date: 1989

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

stationary sequencemixing conditionmultivariate extreme value theory

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Characterization and structure theory for multivariate probability distributions; copulas (62H05) Order statistics; empirical distribution functions (62G30) Stationary stochastic processes (60G10) Limit theorems in probability theory (60F99)

Related Items (24)

The multivariate extremal index and the dependence structure of a multivariate extreme value distribution ⋮ Rank-based inference for bivariate extreme-value copulas ⋮ Maxima of bivariate random vectors: Between independence and complete dependence ⋮ Copula structured M4 processes with application to high-frequency financial data ⋮ Multiple block sizes and overlapping blocks for multivariate time series extremes ⋮ Clustering of Markov chain exceedances ⋮ Sparse moving maxima models for tail dependence in multivariate financial time series ⋮ On the maximum of a bivariate INMA model with integer innovations ⋮ Dependence between two multivariate extremes ⋮ Multivariate extreme values in stationary random sequences ⋮ Asymptotics of joint maxima for discontinuous random variables ⋮ New estimators of the Pickands dependence function and a test for extreme-value dependence ⋮ Asymptotically (in)dependent multivariate maxima of moving maxima process ⋮ Extreme value copula estimation based on block maxima of a multivariate stationary time series ⋮ Asymptotics of Markov Kernels and the Tail Chain ⋮ On the Multivariate Upcrossings Index ⋮ Measuring the extremal dependence ⋮ Estimating the multivariate extremal index function ⋮ Regular variation and related results for the multivariate GARCH\((p,q)\) model with constant conditional correlations ⋮ Rare events, temporal dependence, and the extremal index ⋮ Extremes of space-time Gaussian processes ⋮ Estimation of Pickands dependence function of bivariate extremes under mixing conditions ⋮ Asymptotic dependence of bivariate maxima ⋮ Multivariate extreme values in \(T\)-periodic random sequences under mild oscillation restrictions

Cites Work

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• Bivariate extreme statistics. I
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• Point processes and multivariate extreme values
• Multivariate extreme value distributions for stationary Gaussian sequences
• Maxima and minima of stationary sequences
• A note on the asymptotic independence of high level crossings for dependent Gaussian processes
• Convergence to bivariate limiting extreme value distributions
• Limit laws for the maximum and minimum of stationary sequences
• Asymptotic Independence of Vector Components of Multivariate Extreme Order Statistics
• Max-infinite divisibility
• Limit theory for multivariate sample extremes
• Extreme Values in Uniformly Mixing Stationary Stochastic Processes
• On extreme values in stationary sequences
• Limit Theorems for the Maximum Term in Stationary Sequences
• Extreme Values in Samples from $m$-Dependent Stationary Stochastic Processes

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