In the case of a large portfolio, the existing models of time-varying multivariate volatility are either too simple from the financial perspective or too complex from the numerical angle. Thus, in the paper a new hybrid class of models for n-variate financial time series is proposed. The hybrid specifications are based on two simple structures: the stochastic discount factor model (SDF) from the MSV class and the scalar BEKK(1,1) model from the MGARCH class. Type I and II hybrid models are defined; both allow for different dynamics of each conditional variance or covariance (like BEKK) and keep just one latent process in the conditional covariance matrix in order to describe outliers (like SDF). For the purpose of Bayesian posterior and predictive analyses, the simulation approach based on Gibbs sampling is proposed and approximations unavoidable in the case of large n are suggested.
Bayesian econometrics, Gibbs sampling, time-varying volatility, multivariate GARCH processes, multivariate SV processes
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