Abstract
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 over the state-of-the-arts methods.
Highlights
A well known stylized fact in financial econometrics states that the dynamics of conditional volatility are state dependent since they are affected by the long-run level of volatility itself
It is worth noting that the sCW-GARCH model can be seen as a state-dependent dynamic volatility model with a continuous state space where, at time t, the current value of the state is determined by the smooth memberships τt,s
Since we assume that at each time point the time series model (1) (or (4)) does interact with the current values of {Dt,s,j}, we propose to simplify the estimation in two separate steps: Step 1: Step 2: using cross-sectional data on realized volatility, at each time period the parameter θt is estimated based on Maximum Likelihood (ML)
Summary
A well known stylized fact in financial econometrics states that the dynamics of conditional volatility are state dependent since they are affected by the (latent) long-run level of volatility itself This issue has motivated a variety of time varying extensions of the standard GARCH class of models including latent state regime-switching models (Gallo and Otranto 2018; Hamilton and Susmel 1994; Marcucci 2005), observation-driven regime switching models (Bauwens and Storti 2009, WGARCH), Generalized Autoregressive Score (Creal et al 2013, GAS) models, Component GARCH models (Engle et al 2013, GARCH-MIDAS), (Engle and Rangel 2008, Spline-GARCH).
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