Published online by Cambridge University Press: 13 September 2010
A multivariate extension of the exponential continuous time GARCH (p, q) model (ECOGARCH) is introduced and studied. Stationarity and mixing properties of the new stochastic volatility model are investigated, and ways to model a component-wise leverage effect are presented.
The authors are grateful to the editor and two anonymous referees for their very good comments and also to Claudia Klüppelberg and Jean Jacod for their helpful remarks on a draft of this paper. The second author acknowledges financial support from the Deutsche Forschungsgemeinschaft through the graduate program Angewandte Algorithmische Mathematik at the Technische Universität München during the initial work on the contents of this paper.