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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.

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Bibliographic Info

Paper provided by University of St. Gallen, School of Finance in its series Working Papers on Finance with number 1211.

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Length: 30 pages
Date of creation: Nov 2012
Date of revision:
Handle: RePEc:usg:sfwpfi:2012:11

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  1. Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(2), pages 123-130, March.
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Citations

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Cited by:
  1. Bonato, Matteo & Caporin, Massimiliano & Ranaldo, Angelo, 2013. "Risk spillovers in international equity portfolios," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 121-137.
  2. Caporin, M. & McAleer, M.J., 2010. "Ranking multivariate GARCH models by problem dimension," Econometric Institute Research Papers EI 2010-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2012. "Financial Risk Measurement for Financial Risk Management," NBER Working Papers 18084, National Bureau of Economic Research, Inc.
  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," CIRJE F-Series CIRJE-F-638, CIRJE, Faculty of Economics, University of Tokyo.
  6. Hautsch, Nikolaus & Kyj, Lada M. & Hautsch, Nikolaus, 2009. "A blocking and regularization approach to high dimensional realized covariance estimation," CFS Working Paper Series 2009/20, Center for Financial Studies (CFS).
  7. 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).
  8. Valeri Voev, 2009. "On the Economic Evaluation of Volatility Forecasts," CREATES Research Papers 2009-56, School of Economics and Management, University of Aarhus.

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