New Approach in Dealing with the Non-Negativity of the Conditional Variance in the Estimation of GARCH Model

In this paper, we propose a robust estimation of the conditional variance of the GARCH(1,1) model with respect to the non-negativity constraint against parameter sign. Conditions of second order stationary as well as the existence of moments are given for the new relaxed GARCH(1,1) model whose conditional variance is estimated deriving firstly the unconstrained estimation of the conditional variance from the GARCH(1,1) state space model, then, the robustification is implemented by the Kalman filter outcomes via density function truncation method. The GARCH(1,1) parameters are subsequently estimated by the quasi-maximum likelihood, using the simultaneous perturbation stochastic approximation, based, first, on the Gaussian distribution and, second, on the Student-t distribution. The proposed approach seems to be efficient in improving the accuracy of the quasi-maximum likelihood estimation of GARCH model parameters, in particular, with a prior boundedness information on volatility.