The inhomogeneity of the cross-sectional distribution of realized assets’ volatility is explored and used to build a novel class of GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models. The inhomogeneity of the cross-sectional distribution of realized volatility is captured by a finite Gaussian mixture model plus a uniform component that represents abnormal variations in volatility. Based on the cross-sectional mixture model, at each time point, memberships of assets to risk groups are retrieved via maximum likelihood estimation, as well as the probability that an asset belongs to a specific risk group. The latter is profitably used for specifying a state-dependent model for volatility forecasting. We propose novel GARCH-type specifications the parameters of which act “clusterwise” conditional on past information on the volatility clusters. The empirical performance of the proposed models is assessed by means of an application to a panel of U.S. stocks traded on the NYSE. An extensive forecasting experiment shows that, when the main goal is to improve overall many univariate volatility forecasts, the method proposed in this paper has some advantages bover the state-of-the-arts methods.
A Gaussian Mixture PHD Filter for Jump Markov System Models
