An application of the analogy between vector ARCH and vector random coefficient autoregressive models

In this paper we derive conditions for the conditional covariance matrix to be positive definite in a general vector ARCH model. The conditions can be easily extended to the diagonal vector GARCH model. For the general vector GARCH model, analytical expressions for the conditions in terms of the parameters become complicated, but their validity can in principle be checked numerically once the values of the parameters are given. -- conditional covariance matrix ; multivariate GARCH ; multivariate volatility model ; random coefficient model ; volatility forecasting