A multivariate GARCH model for exchange rates volatility.
The paper presents some recent results on multivariate GARCH models, and proposes a parametrization which guarantees a positive definite conditional variance-covariance matrix of the disturbances. The properties of quasi-maximum likelihood estimators are showed. The latter are, in the multivariate GARCH models, consistent and asymptotically normal. Moreover it is shown the condition to have persistence in variance. The paper contains an empirical application to three weekly exchange rates series (Lira-DM, Lira-USD, Lira-BP) for the period 1973-92. A VAR(3) for the differenced series with GARCH(1,1) disturbances has been identified, and estimated for three periods (1973-79, 1979-85, 1985-92). With the last model (1985-92) one, two and three steps forecats ahead are carried out. This exercise illustrates the forecast features of GARCH models.
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