Distance Correlation and Multivariate Extremes

Specialeforsvar Ved Marie Kryger

Titel: Distance Correlation and Multivariate Extremes

Abstract: The notion of multivariate regular variation implies that the radial and spherical components of a vector become independent when |X| becomes sufficiently large. By using distance correlation as a measure of dependence, this thesis introduces a graphical tool which attempts to propose a sufficiently high threshold such that this asymptotic independence manifests in the data. To gain some insight how to interpret the results, we first consider three examples designed to provide some intuition as to how distance correlation works as a dependence measure for regularly varying random vectors. Thereafter, we expand our analysis and apply the tool on the lagged vectors of the daily log-returns of the S&P500 series. 

Vejleder: Thomas Mikosch
Censor:   Mette M Havning