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Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility

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  • Jacek Osiewalski

    (Department of Econometrics and Operations Research, Cracow University of Economics and Andrzej Frycz Modrzewski Cracow Academy)

  • Anna Pajor

    (Department of Econometrics and Operations Research, Cracow University of Economics)

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).

Suggested Citation

  • Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(2), pages 179-202, November.
    • Handle: RePEc:psc:journl:v:1:y:2009:i:2:p:179-202
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    References listed on IDEAS

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    5. David Chan & Robert Kohn & Chris Kirby, 2006. "Multivariate Stochastic Volatility Models with Correlated Errors," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 245-274.
    6. Osiewalski, Jacek & Pipien, Mateusz, 2004. "Bayesian comparison of bivariate ARCH-type models for the main exchange rates in Poland," Journal of Econometrics, Elsevier, vol. 123(2), pages 371-391, December.
    7. Anna Pajor, 2005. "Bayesian Analysis of Stochastic Volatility Model and Portfolio Allocation," FindEcon Chapters: Forecasting Financial Markets and Economic Decision-Making, in: Władysław Milo & Piotr Wdowiński (ed.), Acta Universitatis Lodziensis. Folia Oeconomica nr 192/2005 - Issues in Modeling, Forecasting and Decision-Making in Financial Markets, edition 1, volume 127, chapter 14, pages 229-249, University of Lodz.
    8. Michael Smith & Andrew Pitts, 2006. "Foreign Exchange Intervention by the Bank of Japan: Bayesian Analysis Using a Bivariate Stochastic Volatility Model," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 425-451.
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    Citations

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    Cited by:

    1. Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    2. Silvennoinen Annastiina & Teräsvirta Timo, 2016. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 347-364, September.
    3. Jacek Osiewalski & Krzysztof Osiewalski, 2016. "Hybrid MSV-MGARCH Models – General Remarks and the GMSF-SBEKK Specification," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 8(4), pages 241-271, December.
    4. Pajor Anna & Wróblewska Justyna, 2017. "VEC-MSF models in Bayesian analysis of short- and long-run relationships," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(3), pages 1-22, June.
    5. Anna Pajor & Justyna Wróblewska, 2022. "Forecasting performance of Bayesian VEC-MSF models for financial data in the presence of long-run relationships," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 427-448, September.
    6. Jacek Osiewalski & Anna Pajor, 2010. "Bayesian Value-at-Risk for a Portfolio: Multi- and Univariate Approaches Using MSF-SBEKK Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 2(4), pages 253-277, September.
    7. Krzysztof Osiewalski & Jacek Osiewalski, 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, Central European Journal of Economic Modelling and Econometrics, vol. 5(1), pages 65-83, March.
    8. Marek A. Dąbrowski & Łukasz Kwiatkowski & Justyna Wróblewska, 2020. "Sources of Real Exchange Rate Variability in Central and Eastern European Countries: Evidence from Structural Bayesian MSH-VAR Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(4), pages 369-412, December.
    9. Darolles, Serge & Francq, Christian & Laurent, Sébastien, 2018. "Asymptotics of Cholesky GARCH models and time-varying conditional betas," Journal of Econometrics, Elsevier, vol. 204(2), pages 223-247.
    10. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    11. Mateusz Pipień, 2013. "Orthogonal Transformation of Coordinates in Copula M-GARCH Models – Bayesian analysis for WIG20 spot and futures returns," NBP Working Papers 151, Narodowy Bank Polski.
    12. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    13. Justyna Wróblewska & Anna Pajor, 2019. "One-period joint forecasts of Polish inflation, unemployment and interest rate using Bayesian VEC-MSF models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 11(1), pages 23-45, March.
    14. Anna Pajor, 2011. "Bayesian Optimal Portfolio Selection in the MSF-SBEKK Model," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 11, pages 41-54.
    15. Justyna Mokrzycka, 2019. "Bayesian comparison of bivariate Copula-GARCH and MGARCH models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 11(1), pages 47-71, March.

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    More about this item

    Keywords

    Bayesian econometrics; Gibbs sampling; time-varying volatility; multivariate GARCH processes; multivariate SV processes;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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