engleski

Properties and Estimation of GARCH(1, 1) Model

We study in depth the properties of the GARCH(1, 1) model and the assumption on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH process are heavily-tailed. We investigated the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1, 1) model. A bounded conditional fourth moment of the rescaled variable (the ratio of the disturbance to the conditional standard deviation) is sufficient for the result. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariancematrix.

GARCH(1; 1) Model; Ergodicity; Strong Stationarity; Consistent Estimation

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