Statistics of multavariate extremes

Specialeforsvar: Thi Huyen Trang Tran

Titel: Statistics of multivariate extremes 

Abstract: In this thesis, we introduce extreme value theory for both univariate and mul- tivariate data. Two stock market indices are used with daily data from around 2010 to 2020 to exemplify the methods. These are purposely covering the start of the COVID-19 crisis, from March to July 2020. We give examples of different dependence methods and measures throughout the text.
We study time dependence between extremes with the extremogram and cross- extremogram. By combining these extremograms with the spectral measure, we may distinguish more easily between negative correlation and independence in some multivariate cases.
We also try to use the theory to detect daily serial dependence. This is done by comparing the analysis with a similar one where we shift the returns of OMX by one day. We make a short investigation of the companies containing the background and the connection between them.
Keywords: Hill estimator, mean excess function, multivariate regular variation, spectral measure, extremal dependence, financial time series

Vejleder:  Thomas Mikosch
censor:     Mette Havning