Statistics of Multivariate Extremes – University of Copenhagen

Statistics of Multivariate Extremes

Specialeforsvar ved Sara Sally Jensen

Titel: Statistics of Multivariate Extremes 

Abstract: We introduce extreme value theory for both univariate and multivariate data. The theory we introduce is concerned with the Hill estimator, mean excess function, the angular density and extremograms. We also illustrate the theory by simulated data. We introduce three different ways of estimating the extremal index to see which method works best. The theory is then used on a dataset of stocks containing daily data from 2005 to 2015 for the companies MetLife Inc and JP Morgan Chase & Co. The time period covers the financial crisis which we know to have caused some extremal dependence. We try to use the theory to detect whether the stocks are dependent. If there is dependence between the companies, we want to figure out if it is external and try to detect daily serial dependence. This is done by comparing the analysis with a similar one where we shift the returns of MetLife Inc by one day. We make a short investigation of the companies containing the background and the connection between them. We also try to find some of the specific days affecting the stocks. Keywords Hill estimator, mean excess function, angular density, extremograms, dependence

 

Vejleder:  Thomas Mikosch
Censor:    Mette Havning