Measuring extremal dependence in financial time series
Vortrag von Prof. Dr. Thomas Mikosch Datum: 18.10.13 Zeit: 10.00 - 10.50 Raum: Y27H46
Covariances are not very meaningful if one wants to study
the extremes in a non-Gaussian time series. However, the tail dependence
coefficient of a two-dimensional vector has been studied in quantitative
risk management for a long time (see e.g. the book by McNeil, Frey and
Embrechts): it can be interpreted as the limiting correlation of the
indicator functions of the extreme event that both components of
the vector are large at the same time. Starting from this observation,
one can introduce an asymptotic autocorrelation function for extreme
events in a time series, the extremogram. The extremogram is essentialy
dimensionless and can be defined for multivariate or even function-valued
data. Based on this idea, the notions of classical
time series analysis enter: short and long range dependence,
autocorrelation function, spectral distribution and their statistical
counterparts such as the sample extremogram and the periodogram of
the extreme events in a series. We explain the underlying theory and
illustrate how the theory works on financial time series.
This is joint work with Richard A. Davis (Columbia) and Yuwei Zhao
(Copenhagen).