Multivariate Mixed Normal Conditional Heteroskedasticity

CORE Discussion Paper No. 2006/12

23 Pages Posted: 15 Jul 2006

See all articles by Luc Bauwens

Luc Bauwens

Université catholique de Louvain

Christian Hafner

Catholic University of Louvain (UCL) - School of Statistics; Tinbergen Institute

J. V. K. Rombouts

HEC Montreal; Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE); Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE); Center for Interuniversity Research and Analysis on Organization (CIRANO)

Date Written: February 2006

Abstract

We propose a new multivariate volatility model where the conditional distribution of a vector time series is given by a mixture of multivariate normal distributions. Each of these distributions is allowed to have a time-varying covariance matrix. The process can be globally covariance-stationary even though some components are not covariance-stationary. We derive some theoretical properties of the model such as the unconditional covariance matrix and autocorrelations of squared returns. The complexity of the model requires a powerful estimation algorithm. In a simulation study we compare estimation by maximum likelihood with the EM algorithm and Bayesian estimation with a Gibbs sampler. Finally, we apply the model to daily U.S. stock returns.

Keywords: Multivariate volatility, Finite mixture, EM algorithm, Bayesian inference

JEL Classification: C11, C22, C52

Suggested Citation

Bauwens, Luc and Hafner, Christian and Rombouts, Jeroen, Multivariate Mixed Normal Conditional Heteroskedasticity (February 2006). CORE Discussion Paper No. 2006/12, Available at SSRN: https://ssrn.com/abstract=914148 or http://dx.doi.org/10.2139/ssrn.914148

Luc Bauwens (Contact Author)

Université catholique de Louvain ( email )

CORE
34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium
32 10 474321 (Phone)
32 10 474301 (Fax)

Christian Hafner

Catholic University of Louvain (UCL) - School of Statistics ( email )

Voie du Roman Pay
34 B-1348 Louvain-La-Neuve, 1348
Belgium

Tinbergen Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Jeroen Rombouts

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE) ( email )

Pavillon De Sève
Ste-Foy, Quebec G1K 7P4
Canada

Center for Interuniversity Research and Analysis on Organization (CIRANO) ( email )

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Montreal H3C 3J7, Quebec
Canada

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