Flexible Multivariate GARCH Modeling with an Application to International Stock Markets

Posted: 19 Oct 2002

See all articles by Olivier Ledoit

Olivier Ledoit

University of Zurich - Department of Economics

Pedro Santa-Clara

New University of Lisbon - Nova School of Business and Economics; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR)

Michael Wolf

University of Zurich - Department of Economics

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Abstract

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in practice. Our model of choice is the Diagonal-Vech version of the Multivariate GARCH(1,1) model. The problem is that the estimation of the general Diagonal-Vech model model is numerically infeasible in dimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contribution is to propose an alternative estimation method that is numerically feasible, produces positive semi-definite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator to a number of existing ones.

Keywords: Diagonal-Vech model multivariate GARCH, unrestricted estimation

JEL Classification: C13, C51, C61, G11, G15

Suggested Citation

Ledoit, Olivier and Santa-Clara, Pedro and Wolf, Michael, Flexible Multivariate GARCH Modeling with an Application to International Stock Markets. Review of Economics and Statistics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=340840

Olivier Ledoit

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Z├╝rich, 8032
Switzerland

Pedro Santa-Clara

New University of Lisbon - Nova School of Business and Economics ( email )

Lisbon
Portugal

HOME PAGE: http://docentes.fe.unl.pt/~psc/

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Michael Wolf (Contact Author)

University of Zurich - Department of Economics ( email )

Wilfriedstrasse 6
Zurich, 8032
Switzerland

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