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## Central European Journal of Economic Modelling and Econometrics (CEJEME)

2019 | 11 | nr 3 | 173--197
Tytuł artykułu

### On Sensitivity of Inference in Bayesian MSF-MGARCH Models

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $H_{t}$ by a scalar random variable $g_{t}$ such that ${ln g_{t}, t\in Z}$ is a Gaussian AR(1) latent process with auto-regression parameter $\phi$. Here we also consider an IG-MSF-MGARCH specification, which is a hybrid generalisation of conditionally Student t MGARCH models, since the latent process ${g_{t}}$ is no longer marginally log-normal (LN), but for $\phi$ = 0 it leads to an inverted gamma (IG) distribution for gt and to the t-MGARCH case. If $\phi$ 6= 0, the latent variables $g_{t}$ 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 $\phi$ - even so low that they can justify the popular t-MGARCH model. (original abstract)
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PL
EN
Rocznik
Tom
Numer
Strony
173--197
Opis fizyczny
Twórcy
autor
• Cracow University of Economics, Poland
autor
• Cracow University of Economics, Jagiellonian University, Poland
Bibliografia
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• [10] Osiewalski J., Osiewalski K., (2016), Hybrid MSV-MGARCH models - general remarks and the GMSF-SBEKK specification, Central European Journal of Economic Modelling and Econometrics 8, 241-271.
• [11] Osiewalski J., Pajor A., (2007), Flexibility and parsimony in multivariate financial modelling: a hybrid bivariate DCC-SV model, [in:] Financial Markets. Principles of Modeling, Forecasting and Decision-Making (FindEcon Monograph Series No.3), [ed.:] W. Milo, P. Wdowiński, Łódź University Press, Łódź, 11-26.
• [12] Osiewalski J., Pajor A., (2009), Bayesian analysis for hybrid MSF-SBEKK models of multivariate volatility, Central European Journal of Economic Modelling and Econometrics 1, 179-202.
• [13] Osiewalski J., Pajor A., (2010), Bayesian Value-at-Risk for a portfolio: multi- and univariate approaches using MSF-SBEKK models, Central European Journal of Economic Modelling and Econometrics 2, 253-277.
• [14] Osiewalski J., Pajor A., (2018), A hybrid MSV-MGARCH generalisation of the tMGARCH model, The 12th Professor Aleksander Zelias International Conference on Modelling and Forecasting of Socio-Economic Phenomena - Conference Proceedings 1, 345-354.
• [15] Osiewalski K., Osiewalski J., (2013), A long-run relationship between daily prices on two markets: the Bayesian VAR(2)-MSF-SBEKK model, Central European Journal of Economic Modelling and Econometrics 5, 65-83.
• [16] Pajor A., (2010), Wielowymiarowe procesy wariancji stochastycznej w ekonometrii finansowej. Ujęcie bayesowskie, Cracow University of Economics, Kraków.
• [17] Pajor A., (2014), Konstrukcja optymalnego portfela w bayesowskim modelu MSF-SBEKK. Portfele funduszy inwestycyjnych PKO TFI, Bank i Kredyt (Bank & Credit) 43, 53-77.
• [18] Pajor A., (2017), Estimating the marginal likelihood using the arithmetic mean identity, Bayesian Analysis 12, 261-287.
• [19] Pajor A., Osiewalski J., (2012), Bayesian Value-at-Risk and Expected Shortfall for a large portfolio (multi- and univariate approaches), Acta Physica Polonica A 121, 2-B, B-101-B-109.
• [20] Pajor A., Wróblewska J., (2017), VEC-MSF models in Bayesian analysis of shortand long-run relationships, Studies in Nonlinear Dynamics and Econometrics 21(3), 1-22.
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• [22] Wróblewska J., Pajor A., (2019), One-period joint forecasts of Polish inflation, unemployment and interest rate using Bayesian VEC-MSF models, Central European Journal of Economic Modeling and Econometrics, 11(1), 23-45.
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