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

Abstract

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.