Application of Extremal Dependence Methods – University of Copenhagen

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Application of Extremal Dependence Methods

Specialeforsvar ved Anders Nygaard Therkelsen

Titel: Application of Extremal Dependence Methods

  

Abstract:
We start with a short introduction to some of the results from univariate extreme value theory used throughout. Two Danish stocks are used with daily data from around 2000 to 2017 to exemplify the methods. These are purposely covering the financial crisis of 2008 about equally before and after. We give examples of the different dependence methods and measures throughout the text. For the investigation of extremal dependence methods, the financial crisis is a great event due to the many extreme events caused by it. We study time dependence between extremes with the extremogram and cross-extremogram. Then we comment on the use of combining these extremograms with the so-called spectral measure. In this way we may distinguish more easily between negative correlation and independence in some multivariate cases. We also introduce a novel heuristic graphical tool. This tool is meant to assist the interpretation and use of the spectral measure for multivariate regularly varying random vectors. Finally, we look at elliptical distributions and specifically a test of ellipticity originally suggested by Hult et al. (2012). Keywords: Multivariate regular variation, spectral measure, extremal dependence, elliptical distributions 

 

 

Vejleder:  Thomas Mikosch
Censor:    Mette M. Havning