2013-2014 Focus Year on "Measures of Dependence"

Workshop on Measures of Extremal Dependence
May 3rd, 2013

1:10-2:00 Thomas Mikosch, University of Copenhagen
Title: Measuring serial extremal dependence with the extremogram

Abstract: The extremogram is an analog of the autocorrelation function in a strictly stationary time series. It is motivated by the tail dependence coefficient introduced in quantitative risk management for pairs of random variables. At a given lag h, the extremogram measures the probability of an extreme event, given that an extreme event happened at time zero.
We discuss the theoretical framework of the extremogram; in this context regular variaton of the finite-dimensional distributions is a reasonable assumption. We also consider the sample extremogram and discuss its asymptotic properties. Finally, we use the similarities between the extremogram and the autocorrelation functions of a stationary sequence for some Fourier analysis of extreme events. The content of the talk is based on joint work with Richard Davis (Bernouli 2009, J. Econometrics 2012) and Yuwei Zhao (Bernoulli 2013).