Essentials of Time Series for Financial Applications

(6.63)

Note that Eq. (6.63) guarantees by construction that ${\rho }_{ij,t+1|t}\in [-1,1]$. Clearly, in the GARCH(1,1) case, ${\overline{\rho }}_{ij}={\omega }_{ij}/(1-\alpha -\beta )$. Interestingly, only the intercept parameter ${\omega }_{ij}$ is allowed to differ across different pairs of assets: also in this case, $\alpha$ and $\beta$ are common across different pairs of assets; the same occurs for the single parameter $\lambda$