• Bernoulli
  • Volume 15, Number 4 (2009), 977-1009.

The extremogram: A correlogram for extreme events

Richard A. Davis and Thomas Mikosch

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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 others, ARMA processes with regularly varying noise, GARCH processes with normally or Student-distributed noise and stochastic volatility models with regularly varying multiplicative noise. We define an analog of the autocorrelation function, the extremogram, which depends only on the extreme values in the sequence. We also propose a natural estimator for the extremogram and study its asymptotic properties under $α$-mixing. We show asymptotic normality, calculate the extremogram for various examples and consider spectral analysis related to the extremogram.

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Bernoulli, Volume 15, Number 4 (2009), 977-1009.

First available in Project Euclid: 8 January 2010

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GARCH multivariate regular variation stationary sequence stochastic volatility process tail dependence coefficient


Davis, Richard A.; Mikosch, Thomas. The extremogram: A correlogram for extreme events. Bernoulli 15 (2009), no. 4, 977--1009. doi:10.3150/09-BEJ213.

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