The extremogram: A correlogram for extreme events

Richard A. Davis, Thomas Mikosch
2009 Bernoulli  
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
more » ... e extreme values in the sequence. We also propose a natural estimator for the extremogram and study its asymptotic properties under $\alpha$-mixing. We show asymptotic normality, calculate the extremogram for various examples and consider spectral analysis related to the extremogram.
doi:10.3150/09-bej213 fatcat:n5rjwgt3grdz5kjch7p2e6gpsq