FIN-01-027

Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH

September 7, 2001

Robert F. Engle and Kevin Sheppard

ABSTRACT

In this paper, we develop the theoretical and empirical properties of a new class of multivariate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance estimation can be simplified by estimating univariate GARCH models for each asset, and then, using transformed residuals resulting from the first stage, estimating a conditional correlation estimator. The standard errors for the first stage parameters remain consistent, and only the standard errors for the correlation parameters need to be modified. We use the model to estimate the conditional covariance of up to 100 assets using S&P 500 Sector Indices and Dow Jones Industrial Average stocks, and conduct specification tests of the estimator using an industry standard benchmark for volatility models. This new estimator demonstrates very strong performance especially considering ease of implementation of the estimator.

Classification: C32, G0, G1

Robert F. Engle
Institution: Stern School of Business, New York University, 44th West 4th Street, New York, NY 10012
Telephone: (212) 998-0710
Fax: (212) 995-4220
Email: rengle@stern.nyu.edu
Homepage:http://www.stern.nyu.edu/~rengle

Kevin Sheppard
Institution: Department of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0505, USA
Email: kksheppard@ucsd.edu

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