Here some various GARCH models :
The QGARCH process introduced by Engle and Ng (1993) and Sentana (1995) allows to take into account the asymmetries in the response of the conditional volatility innovations. Sentana (1995) showed that the properties of the GARCH (1,1) and QGARCH (1.1) are very similar: the stationarity conditions are identical to those derived in the case of GARCH and as the residue is a process centered, the expression of his unconditional expectation is also identical to that obtained with a GARCH. However, the kurtosis in QGARCH models is always greater than in the corresponding symmetric GARCH models, which explains the empirically QGARCH often dominates the GARCH.
The GARCH-M model (General Autoregrssive Conditional heteroskedasticity in Mean) was introduced by Engle, Lilien-Robbins (1987). This is an ARCH model to measure the influence of the performance of securities conditional volatility. Such as ARCH linear models, GARCH-M model is based on a quadratic specification of the conditional variance of the disturbance.
The GJR-GARCH model was introduced by Glosten, Jagannathan and Runkle (1993). This is a non-linear GARCH model to account for the asymmetry in the response of the conditional variance to innovation. The logic of this model is similar to models of regime change and more specifically threshold models (Tong, 1990). The principle of the GJR-GARCH model is that the dynamics of the conditional variance admits a regime change which depends on the sign of past innovation.
The IGARCH model (Integrated General Autoregressive Conditional heteroskedasticity) corresponds to the case of a unit root in the conditional variance. This is a non-linear ARCH model characterized by an effect of persistence in variance. That is to say, a shock on the current conditional variance affects all future expected values.
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