## On the computational estimation of high order GARCH model

To guarantee the non-negativity of the conditional variance of the GARCH process, it is sufficient to assume the non-negativity of its parameters. This condition was empirically violated besides rendering the GARCH model more restrictive. It was subsequently relaxed for some GARCH orders by necessary and sufficient constraints. In this paper, we generalized an approach for the QML estimation of the GARCH$(p,q)$ parameters for all orders $p\geq 1$ and $q\ge 1$ using a constrained Kalman filter. Such an approach allows a relaxed QML estimation of the GARCH without th