A simple multivariate ARCH model specified by random coefficients

This paper provides an alternative formulation of the conditional correlation structure in fitting the multivariate GARCH model. A special case is the multivariate ARCH model with random coefficients. Its coherence structure is derived by the correlations between the random coefficients which play an important role in describing the interested heteroscedastic features. The parameter estimation problem can be solved by maximum likelihood estimation and model selection is via the likelihood ratio test. We consider three real applications: (1) the spot and forward rates of the Deutsche Mark against the US dollars; (2) exchange rates of Deutsche Mark and Japanese Yen against US dollars; (3) the Heng Sang index and SES index.