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Forecasting Realized (Co)Variances with a Bloc Structure Wishart Autoregressive Model

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  • Bonato, Matteo

    ()

  • Caporin, Massimiliano

    ()

  • Ranaldo, Angelo

    ()

Abstract

The increased availability of high-frequency data provides new tools for forecasting of variances and covariances between assets. However, recent realized (co)variance models may suffer from a 'curse of dimensionality' problem similar to that of multivariate GARCH specifications. As a result, they need strong parameter restrictions, in order to avoid non-interpretability of model coefficients, as in the matrix and log exponential representations. Among the proposed models, the Wishart autoregressive model introduced by Gourieroux et al. (2007) analyzes the realized covariance matrices without any restriction on the parameters while maintaining coeffcient interpretability. Indeed, the model, under mild stationarity conditions, provides positive deffinite forecasts for the realized covariance matrices. Unfortunately, it is still not feasible for large asset cross-section dimensions. In this paper we propose a restricted parametrization of the Wishart Autoregressive model which is feasible even with a large cross-section of assets. In particular, we assume that the asset variances-covariances have no or limited spillover and that their dynamic is sector-specific. In addition, we propose a Wishart-based generalization of the HAR model of Corsi (2004). We present an empirical application based on variance forecasting and risk evaluation of a portfolio of two US treasury bills and two exchange rates. We compare our restricted specifications with the traditional WAR parameterizations. Our results show that the restrictions may be supported by the data and that the risk evaluations of the models are extremely close. This confirms that our model can be safely used in a large cross-sectional dimension given that it provides results similar to fully parameterized specifications.

Suggested Citation

  • Bonato, Matteo & Caporin, Massimiliano & Ranaldo, Angelo, 2012. "Forecasting Realized (Co)Variances with a Bloc Structure Wishart Autoregressive Model," Working Papers on Finance 1211, University of St. Gallen, School of Finance.
  • Handle: RePEc:usg:sfwpfi:2012:11
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    Cited by:

    1. Fengler, Matthias R. & Gisler, Katja I.M., 2015. "A variance spillover analysis without covariances: What do we miss?," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 174-195.
    2. Massimiliano Caporin & Michael McAleer, 2011. "Ranking Multivariate GARCH Models by Problem Dimension: An Empirical Evaluation," Documentos de Trabajo del ICAE 2011-20, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Varneskov, Rasmus & Voev, Valeri, 2013. "The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 83-95.
    4. 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).
    5. Massimiliano Caporin & Michael McAleer, 2009. "Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models," Documentos de Trabajo del ICAE 2009-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," "Marco Fanno" Working Papers 0124, Dipartimento di Scienze Economiche "Marco Fanno".
    7. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, vol. 167(1), pages 211-223.
    8. Bonato, Matteo & Caporin, Massimiliano & Ranaldo, Angelo, 2013. "Risk spillovers in international equity portfolios," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 121-137.
    9. Nikolaus Hautsch & Lada M. Kyj & Roel C. A. Oomen, 2012. "A blocking and regularization approach to high‐dimensional realized covariance estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(4), pages 625-645, June.
    10. 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).
    11. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    12. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    13. 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.
    14. Valeri Voev, 2009. "On the Economic Evaluation of Volatility Forecasts," CREATES Research Papers 2009-56, Department of Economics and Business Economics, Aarhus University.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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