Asymmetric Multivariate Normal Mixture GARCH

Posted: 20 Feb 2008

See all articles by Markus Haas

Markus Haas

University of Kiel - Faculty of Economics and Social Sciences

Stefan Mittnik

University of Kiel - Institute of Statistics & Econometrics; Ludwig Maximilian University of Munich (LMU) - Faculty of Economics; CESifo (Center for Economic Studies and Ifo Institute)

Marc S. Paolella

University of Zurich - Department Finance; Swiss Finance Institute

Date Written: February 2008

Abstract

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is shown that the disaggregation of the conditional (co)variance process generated by the model provides substantial intuition. Moreover, the model exhibits a strong performance in calculating out-of-sample Value-at-Risk measures.

Keywords: Conditional Volatility, Finite Normal Mixtures, Multivariate GARCH, Leverage Effect

JEL Classification: C32, C51, G10, G11

Suggested Citation

Haas, Markus and Mittnik, Stefan and Paolella, Marc S., Asymmetric Multivariate Normal Mixture GARCH (February 2008). CFS Working Paper No. 2008/07, Available at SSRN: https://ssrn.com/abstract=1095768

Markus Haas (Contact Author)

University of Kiel - Faculty of Economics and Social Sciences ( email )

Kiel
Germany

Stefan Mittnik

University of Kiel - Institute of Statistics & Econometrics ( email )

Olshausenstr. 40
Kiel, Schleswig-Holstein 24118
Germany

Ludwig Maximilian University of Munich (LMU) - Faculty of Economics ( email )

Akademiestr.1/III
Munich, D-80539
Germany

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

Marc S. Paolella

University of Zurich - Department Finance

Plattenstr. 14
Zürich, 8032
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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