Analytic Score for Multivariate GARCH Models
Multivariate GARCH models constitute the workhorse of empirical applications in several fields, a notable example being financial econometrics. Unfortunately, ML (or quasi-ML) estimation of such models, although relatively straightforward in theory, is often made difficult by the fact that available software relies on numerical methods for computing the first derivatives of the log-likelihood; the fact that these models often include several dozens of parameters makes it impractical to estimate even medium-sized models. In this paper, closed-form expressions for the score of the BEKK model of Engle and Kroner (1995) are obtained, and strategies for efficient computation are discussed.
|Date of creation:||Oct 1999|
|Date of revision:|
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- Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
- Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
- Fiorentini,G. & Calzolari,G. & Panattoni,L., 1995.
"Analytic Derivatives and the Computation of Garch Estimates,"
9519, Centro de Estudios Monetarios Y Financieros-.
- Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
- Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
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