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Dynamic Modeling of Large Dimensional Covariance Matrices

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  • Valeri Voev

    ()
    (University of Konstanz)

Abstract

Modelling and forecasting the covariance of financial return series has always been a challange due to the so-called "curse of dimensionality". This paper proposes a methodology that is applicable in large dimensional cases and is based on a time series of realized covariance matrices. Some solutions are also presented to the problem of non-positive definite forecasts. This methodology is then compared to some traditional models on the basis of its forecasting performance employing Diebold-Mariano tests. We show that our approach is better suited to capture the dynamic features of volatilities and covolatilities compared to the sample covariance based models.

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File URL: http://cofe.uni-konstanz.de/Papers/dp07_01.pdf
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Bibliographic Info

Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 07-01.

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Length: 21 pages
Date of creation: 01 Feb 2007
Date of revision:
Handle: RePEc:knz:cofedp:0701

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References

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  1. Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers 586, Department of Economics and Business, Universitat Pompeu Fabra.
  2. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
  3. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," NBER Working Papers 11188, National Bureau of Economic Research, Inc.
  4. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
  5. Valeri Voev & Asger Lunde, 2007. "Integrated Covariance Estimation using High-frequency Data in the Presence of Noise," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 68-104.
  6. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  7. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
  9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  10. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-62, July.
  11. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  12. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  13. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  14. Roel C. A. Oomen, 2005. "Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 555-577.
  15. Bystrom, Hans N. E., 2002. "Using simulated currency rainbow options to evaluate covariance matrix forecasts," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 12(3), pages 216-230, July.
  16. Christian Gourieroux & Joann Jasiak & Razvan Sufana, 2004. "The Wishart Autoregressive of Multivariate Stochastic Volatility," Working Papers 2004-32, Centre de Recherche en Economie et Statistique.
  17. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers 2005_2, York University, Department of Economics.
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Citations

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Cited by:
  1. Tsunehiro Ishihara & Yasuhiro Omori & Manabu Asai, 2011. "Matrix Exponential Stochastic Volatility with Cross Leverage," CIRJE F-Series CIRJE-F-812, CIRJE, Faculty of Economics, University of Tokyo.
  2. Lillie Lam & Laurence Fung & Ip-wing Yu, 2009. "Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes," Working Papers 0901, Hong Kong Monetary Authority.
  3. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2011. "Multivariate High-Frequency-Based Volatility (HEAVY) Models," Economics Series Working Papers 533, University of Oxford, Department of Economics.
  4. Giulio PALOMBA, 2006. "Multivariate GARCH models and Black-Litterman approach for tracking error constrained portfolios: an empirical analysis," Working Papers 267, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

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