Title: An extended GARCH model with two volatility sequences
Authors: Abdelhakim Aknouche - Qassim University (Saudi Arabia) [presenting]
Christian Francq - University of Lille and CREST (France)
Abstract: A GARCH model with two volatility processes (2GARCH) is proposed. The first volatility, unobserved, satisfies an autoregressive conditional duration (ACD) equation based on past squared observations. The second observable (or predictable) volatility is exactly the same as that of a standard GARCH model and is none other than the conditional mean of the unobserved volatility. When the innovation of the ACD process degenerates at one, the two volatilities coincide and the 2GARCH model reduces to the standard GARCH model. Thus the ACD parameters are estimated in a standard way by using the Gaussian quasi-maximum likelihood estimate (QMLE), while the variance of the ACD innovation is consistently estimated by an appropriate weighted least squares method. The unobserved volatility sequence, however, can be estimated using signal extraction methods. Finally, the standard GARCH hypothesis is tested while testing the nullity of the variance of the ACD innovation. From the estimation of various return series (S\&P 500, etc.), it turns out that the standard GARCH hypothesis cannot be reasonably accepted.