Alpha-stable Random Vectors with Time Varying Spectral Measure and Applications to Financial Time Series Analysis

Dissertation an der Fakultät für Mathematik, Informatik und Statistik der Ludwig-Maximilians-Universität München - "Summary: The accurate description of multivariate financial return distributions, which are generally characterized by time varying volatilities, time varying dependencies, and conditional distributions that differ substantially from the Gaussian distribution, is crucial for financial decision making. A generalization of the Gaussian distribution that allows for fat tails and skewness is the stable distribution. This thesis presents various time series models for alpha-stable random vectors with time varying spectral measure taking parameter estimation and empirical applicability - with special emphasis on portfolio optimization and risk assessment - into special consideration.The event study methodology is generalized to allow for heteroscedastic stable error distributions. A factor model for stable random vectors with time varying spectral measure is established, which enables parameter estimation by employing univariate techniques. A simulation approach for calculating the density and distribution function of Sub-Gaussian stable random vectors is developed and used for maximum simulated likelihood estimation. Two conditional covariation models for modeling the dynamics of the spectral measure of conditional Sub-Gaussian random vectors are presented that are natural generalizations of Gaussian conditional correlation models. "