On Sensitivity of Inference in Bayesian MSF-MGARCH Models

Abstract

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 LNMSF-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 also
consider 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 6= 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 the t-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.