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Bayesian Semiparametric Modeling of Realized Covariance Matrices

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  • Jin, Xin
  • Maheu, John M

Abstract

This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined with returns to provide a coherent joint model of returns and RCOV. The extensive forecast results show the new models provide very significant improvements in density forecasts for RCOV and returns and competitive point forecasts of RCOV.

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  • Jin, Xin & Maheu, John M, 2014. "Bayesian Semiparametric Modeling of Realized Covariance Matrices," MPRA Paper 60102, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:60102
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    Cited by:

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    2. Luc Bauwens & Jean-François Carpantier & Arnaud Dufays, 2017. "Autoregressive Moving Average Infinite Hidden Markov-Switching Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 162-182, April.
    3. Fisher, Mark & Jensen, Mark J., 2019. "Bayesian inference and prediction of a multiple-change-point panel model with nonparametric priors," Journal of Econometrics, Elsevier, vol. 210(1), pages 187-202.
    4. Yuta Yamauchi & Yasuhiro Omori, 2018. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," Papers 1809.09928, arXiv.org, revised Mar 2019.
    5. Xin Jin & John M. Maheu & Qiao Yang, 2019. "Bayesian parametric and semiparametric factor models for large realized covariance matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 641-660, August.
    6. Gael M. Martin & David T. Frazier & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2022. "Bayesian Forecasting in Economics and Finance: A Modern Review," Papers 2212.03471, arXiv.org, revised Jul 2023.
    7. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    8. Jin, Xin & Maheu, John M. & Yang, Qiao, 2022. "Infinite Markov pooling of predictive distributions," Journal of Econometrics, Elsevier, vol. 228(2), pages 302-321.
    9. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    10. Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute, revised 11 Jul 2023.
    11. Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
    12. Yuta Yamauchi & Yasuhiro Omori, 2016. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations ," CIRJE F-Series CIRJE-F-1029, CIRJE, Faculty of Economics, University of Tokyo.
    13. Yaojie Zhang & Yu Wei & Li Liu, 2019. "Improving forecasting performance of realized covariance with extensions of HAR-RCOV model: statistical significance and economic value," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1425-1438, September.
    14. Xin Jin & Jia Liu & Qiao Yang, 2021. "Does the Choice of Realized Covariance Measures Empirically Matter? A Bayesian Density Prediction Approach," Econometrics, MDPI, vol. 9(4), pages 1-22, December.
    15. Opschoor, Anne & Lucas, André, 2023. "Time-varying variance and skewness in realized volatility measures," International Journal of Forecasting, Elsevier, vol. 39(2), pages 827-840.
    16. I. G. Ukpong & K. G. Balcombe & I. M. Fraser & F. J. Areal, 2019. "Preferences for Mitigation of the Negative Impacts of the Oil and Gas Industry in the Niger Delta Region of Nigeria," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 74(2), pages 811-843, October.
    17. Yuta yamauchi & Yasuhiro Omori, 2019. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," CIRJE F-Series CIRJE-F-1117, CIRJE, Faculty of Economics, University of Tokyo.
    18. Li, Chenxing, 2022. "A multivariate GARCH model with an infinite hidden Markov mixture," MPRA Paper 112792, University Library of Munich, Germany.
    19. McCausland, William & Miller, Shirley & Pelletier, Denis, 2021. "Multivariate stochastic volatility using the HESSIAN method," Econometrics and Statistics, Elsevier, vol. 17(C), pages 76-94.
    20. Jim Griffin & Maria Kalli & Mark Steel, 2018. "Discussion of “Nonparametric Bayesian Inference in Applications”: Bayesian nonparametric methods in econometrics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 207-218, June.
    21. Li, Chenxing & Maheu, John M & Yang, Qiao, 2022. "An Infinite Hidden Markov Model with Stochastic Volatility," MPRA Paper 115456, University Library of Munich, Germany.

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    More about this item

    Keywords

    multi-period density forecasts; inverse-Wishart distribution; beam sampling; hierarchical Dirichlet process; infinite hidden Markov model;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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