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The conditional autoregressive wishart model for multivariate stock market volatility

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  • Golosnoy, Vasyl
  • Gribisch, Bastian
  • Liesenfeld, Roman

Abstract

We propose a Conditional Autoregressive Wishart (CAW) model for the analysis of realized covariance matrices of asset returns. Our model assumes a generalized linear autoregressive moving average structure for the scale matrix of the Wishart distribution allowing to accommodate for complex dynamic interdependence between the variances and covariances of assets. In addition, it accounts for symmetry and positive definiteness of covariance matrices without imposing parametric restrictions, and can easily be estimated by Maximum Likelihood. We also propose extensions of the CAW model obtained by including a Mixed Data Sampling (MIDAS) component and Heterogeneous Autoregressive (HAR) dynamics for long-run fluctuations. The CAW models are applied to time series of daily realized variances and covariances for five New York Stock Exchange (NYSE) stocks.

Suggested Citation

  • Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2010. "The conditional autoregressive wishart model for multivariate stock market volatility," Economics Working Papers 2010-07, Christian-Albrechts-University of Kiel, Department of Economics.
  • Handle: RePEc:zbw:cauewp:201007
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    Cited by:

    1. Márcio Gomes Pinto Garcia & Marcelo Cunha Medeiros & Francisco Eduardo de Luna e Almeida Santos, 2014. "Economic gains of realized volatility in the Brazilian stock market," Brazilian Review of Finance, Brazilian Society of Finance, vol. 12(3), pages 319-349.
    2. Bauwens, Luc & Braione, Manuela & Storti, Giuseppe, 2017. "A dynamic component model for forecasting high-dimensional realized covariance matrices," Econometrics and Statistics, Elsevier, vol. 1(C), pages 40-61.
    3. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," CORE Discussion Papers 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Braione, Manuela, 2016. "A time-varying long run HEAVY model," Statistics & Probability Letters, Elsevier, pages 36-44.
    5. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    6. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    7. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, pages 251-262.
    8. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    9. Luc Bauwens & Manuela Braione & Giuseppe Storti, 2016. "Forecasting Comparison of Long Term Component Dynamic Models for Realized Covariance Matrices," Annals of Economics and Statistics, GENES, issue 123-124, pages 103-134.
    10. Stanislav Anatolyev & Nikita Kobotaev, 2015. "Modeling and Forecasting Realized Covariance Matrices with Accounting for Leverage," Working Papers w0213, Center for Economic and Financial Research (CEFIR).
    11. Caporin, Massimiliano & Velo, Gabriel G., 2015. "Realized range volatility forecasting: Dynamic features and predictive variables," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 98-112.
    12. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    13. Gribisch, Bastian, 2013. "A latent dynamic factor approach to forecasting multivariate stock market volatility," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79823, Verein für Socialpolitik / German Economic Association.
    14. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, pages 331-350.
    15. Vincenzo Candila, 2013. "A Comparison Of The Forecasting Performances Of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    16. Fengler, Matthias R. & Herwartz, Helmut, 2015. "Measuring spot variance spillovers when (co)variances are time-varying – the case of multivariate GARCH models," Economics Working Paper Series 1517, University of St. Gallen, School of Economics and Political Science.
    17. BAUWENS, Luc & STORTI, Giuseppe, 2012. "Computationally efficient inference procedures for vast dimensional realized covariance models," CORE Discussion Papers 2012028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    19. BAUWENS, Luc & STORTI, Giuseppe & VIOLANTE, Francesco, 2012. "Dynamic conditional correlation models for realized covariance matrices," CORE Discussion Papers 2012060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "Intra-daily volatility spillovers between the US and German stock markets," Economics Working Papers 2012-06, Christian-Albrechts-University of Kiel, Department of Economics.
    21. Kevin Sheppard, 2014. "Factor High-Frequency Based Volatility (HEAVY) Models," Economics Series Working Papers 710, University of Oxford, Department of Economics.
    22. Peter Reinhard Hansen & Pawel Janus & Siem Jan Koopman, 2016. "Realized Wishart-GARCH: A Score-driven Multi-Asset Volatility Model," Tinbergen Institute Discussion Papers 16-061/III, Tinbergen Institute.
    23. Karapanagiotidis, Paul, 2012. "Improving Bayesian VAR density forecasts through autoregressive Wishart Stochastic Volatility," MPRA Paper 38885, University Library of Munich, Germany.
    24. Jin, Xin & Maheu, John M & Yang, Qiao, 2017. "Bayesian Parametric and Semiparametric Factor Models for Large Realized Covariance Matrices," MPRA Paper 81920, University Library of Munich, Germany.
    25. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2015. "Intra-daily volatility spillovers in international stock markets," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 95-114.

    More about this item

    Keywords

    Component volatility models; Covariance matrix; Mixed data sampling; Observation-driven models; Realized volatility;

    JEL classification:

    • 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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