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Abstract

The aim of this paper is to examine the empirical usefulness of two new MSF – Scalar BEKK(1,1) models of n-variate volatility. These models formally belong to the MSV class, but in fact are some hybrids of the simplest MGARCH and MSV specifications. Such hybrid structures have been proposed as feasible (yet non-trivial) tools for analyzing highly dimensional financial data (large n). This research shows Bayesian model comparison for two data sets with n = 2, since in bivariate cases we can obtain Bayes factors against many (even unparsimonious) MGARCH and MSV specifications. Also, for bivariate data, approximate posterior results (based on preliminary estimates of nuisance matrix parameters) are compared to the exact ones in both MSF-SBEKK models. Finally, approximate results are obtained for a large set of returns on equities (n = 34).
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Abstract

Hybrid MSV-MGARCH models, in particular the MSF-SBEKKspecification, proved useful in multivariate modelling of returns on financialand commodity markets. The initial MSF-MGARCH structure, called LN-MSF-MGARCH here, is obtained by multiplying the MGARCH conditionalcovariance matrixHtby a scalar random variablegtsuch that{lngt, t∈Z}is aGaussian AR(1) latent process with auto-regression parameterφ. Here we alsoconsider an IG-MSF-MGARCH specification, which is a hybrid generalisationof conditionally StudenttMGARCH models, since the latent process{gt}is nolonger marginally log-normal (LN), but forφ= 0it leads to an inverted gamma(IG) distribution forgtand to thet-MGARCH case. Ifφ6= 0, the latentvariablesgtare dependent, so (in comparison to thet-MGARCH specification)we get an additional source of dependence and one more parameter. Dueto the existence of latent processes, the Bayesian approach, equipped withMCMC simulation techniques, is a natural and feasible statistical tool to dealwith MSF-MGARCH models. In this paper we show how the distributionalassumptions for the latent process together with the specification of theprior density for its parameters affect posterior results, in particular theones related to adequacy of thet-MGARCH model. Our empirical findingsdemonstrate sensitivity of inference on the latent process and its parameters,but, fortunately, neither on volatility of the returns nor on their conditionalcorrelation. The new IG-MSF-MGARCH specification is based on a morevolatile latent process than the older LN-MSF-MGARCH structure, so thenew one may lead to lower values ofφ– even so low that they can justify thepopulart-MGARCH model.
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Abstract

The paper investigates Bayesian approach to estimate generalized true random-effects models (GTRE). The analysis shows that under suitably defined priors for transient and persistent inefficiency terms the posterior characteristics of such models are well approximated using simple Gibbs sampling. No model re-parameterization is required. The proposed modification not only allows us to make more reasonable (less informative) assumptions as regards prior transient and persistent inefficiency distribution but also appears to be more reliable in handling especially noisy datasets. Empirical application furthers the research into stochastic frontier analysis using GTRE models by examining the relationship between inefficiency terms in GTRE, true random-effects, generalized stochastic frontier and a standard stochastic frontier model.
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