On the computational estimation of high order GARCH model

: pp. 797–806
Received: May 23, 2021
Accepted: June 07, 2021

Mathematical Modeling and Computing, Vol. 8, No. 4, pp. 797–806 (2021)

IPIM, National Schools of Applied Sciences, Khouribga, Sultan Moulay Slimane University, Morocco
IPIM, National Schools of Applied Sciences, Khouribga, Sultan Moulay Slimane University, Morocco
University Mohammed First, Highest School of Technologies, Oujda, Morocco

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 the need to identify and/or apply the relaxed constraints to the parameters.  The performance of our method is demonstrated through Monte Carlo simulations and empirical applications to real data.

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