Hybrid MSV-MGARCH models, in particular the MSF-SBEKK specification,
proved useful in multivariate modelling of returns on financial and
commodity markets. The initial MSF-MGARCH structure, called
LN-MSF-MGARCH here, is obtained by multiplying the MGARCH conditional
covariance matrix Ht by a scalar random variable gt
such that{ln gt, t ∈ Z} is a
Gaussian AR(1) latent process with auto-regression parameter φ.
Here we alsoconsider an IG-MSF-MGARCH specification, which is a hybrid
generalisation of conditionally Student t MGARCH models, since
the latent process {gt} is no longer marginally
log-normal (LN), but for φ = 0 it leads to an inverted gamma
(IG) distribution for gt and to the t-MGARCH
case. If φ =/ 0, the latent variables gt
are dependent, so (in comparison to the t-MGARCH specification)
we get an additional source of dependence and one more parameter. Due to
the existence of latent processes, the Bayesian approach, equipped with
MCMC simulation techniques, is a natural and feasible statistical tool
to deal with MSF-MGARCH models. In this paper we show how the
distributional assumptions for the latent process together with the
specification of the prior density for its parameters affect posterior
results, in particular the ones related to adequacy of thet-MGARCH
model. Our empirical findings demonstrate sensitivity of inference on
the latent process and its parameters, but, fortunately, neither on
volatility of the returns nor on their conditional correlation. The new
IG-MSF-MGARCH specification is based on a more volatile latent process
than the older LN-MSF-MGARCH structure, so the new one may lead to lower
values of φ – even so low that they can justify the popular t-MGARCH
model.