, Volume 19, Issue 2, pp 133-143

Analytical Score for Multivariate GARCH Models

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Abstract

Multivariate GARCH models constitute the workhorse of empiricalapplications in several fields, a notable example being financialeconometrics. Unfortunately, ML (or quasi-ML) estimation of such models,although relatively straightforward in theory, is often made difficult bythe fact that available software relies on numerical methods for computingthe first derivatives of the log-likelihood; the fact that these modelsoften include a large number of parameters makes it impractical toestimate even medium-sized models. In this paper, closed-form expressionsfor the score of the BEKK model of Engle and Kroner (1995) are obtained,and strategies for efficient computation are discussed.