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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-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.
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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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