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Forecasting Covariance Matrices: A Mixed Frequency Approach

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Author Info

  • Roxana Halbleib

    ()
    (Department of Economics, University of Konstanz, Germany)

  • Valeri Voev

    ()
    (School of Economics and Management, Aarhus University, Denmark)

Abstract

In this paper we introduce a new method of forecasting covariance matrices of large dimensions by exploiting the theoretical and empirical potential of using mixed-frequency sampled data. The idea is to use high-frequency (intraday) data to model and forecast daily realized volatilities combined with low frequency (daily) data as input to the correlation model. The main theoretical contribution of the paper is to derive statistical and economic conditions, which ensure that a mixed-frequency forecast has a smaller mean squared forecast error than a similar pure low-frequency or pure high-frequency specification. The conditions are very general and do not rely on distributional assumptions of the forecasting errors or on a particular model specification. Moreover, we provide empirical evidence that, besides overcoming the computational burden of pure high-frequency specifications, the mixed-frequency forecasts are particularly useful in turbulent financial periods, such as the previous financial crisis and always outperforms the pure low-frequency specifications.

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Bibliographic Info

Paper provided by Department of Economics, University of Konstanz in its series Working Paper Series of the Department of Economics, University of Konstanz with number 2012-30.

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Length: 35 pages
Date of creation: 12 Oct 2012
Date of revision:
Handle: RePEc:knz:dpteco:1230

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Keywords: Multivariate volatility; Volatility forecasting; High-frequency data; Realized variance; Realized covariance;

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References

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  1. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2011. "The Merit of High-Frequency Data in Portfolio Allocation," SFB 649 Discussion Papers SFB649DP2011-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Peter R. Hansen & Asger Lunde & Valeri Voev, 2010. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and CoVolatility," CREATES Research Papers 2010-74, School of Economics and Management, University of Aarhus.
  3. Giacomini, Raffaella & White, Halbert, 2003. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series, Department of Economics, UC San Diego qt5jk0j5jh, Department of Economics, UC San Diego.
  4. Neil Shephard & Kevin Sheppard, 2009. "Realising the future: forecasting with high frequency based volatility (HEAVY) models," Economics Papers 2009-W03, Economics Group, Nuffield College, University of Oxford.
  5. 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, 06.
  6. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," CREATES Research Papers 2008-63, School of Economics and Management, University of Aarhus.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  8. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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  10. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Papers 2006-W03, Economics Group, Nuffield College, University of Oxford.
  11. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2009. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," CREATES Research Papers 2009-45, School of Economics and Management, University of Aarhus.
  12. Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CoFE Discussion Paper 08-06, Center of Finance and Econometrics, University of Konstanz.
  13. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 246-256, January.
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  15. 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, American Statistical Association, vol. 20(3), pages 351-62, July.
  16. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
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  21. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, 09.
  22. Ingmar Nolte & Valeri Voev, 2011. "Least Squares Inference on Integrated Volatility and the Relationship Between Efficient Prices and Noise," Journal of Business & Economic Statistics, Taylor & Francis Journals, Taylor & Francis Journals, vol. 30(1), pages 94-108, April.
  23. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, School of Economics and Management, University of Aarhus.
  24. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  25. Fulvio Corsi & Francesco Audrino, 2008. "Modeling Tick-by-Tick Realized Correlations," University of St. Gallen Department of Economics working paper series 2008 2008-05, Department of Economics, University of St. Gallen.
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  29. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C1-C32, November.
  30. BAUWENS, Luc & STORTI, Giuseppe & VIOLANTE, Francesco, 2012. "Dynamic conditional correlation models for realized covariance matrices," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2012060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  31. Hafner, Christian M. & Reznikova, Olga, 2012. "On the estimation of dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3533-3545.
  32. Ingmar Nolte & Valeri Voev, 2007. "Estimating High-Frequency Based (Co-) Variances: A Unified Approach," CoFE Discussion Paper 07-07, Center of Finance and Econometrics, University of Konstanz.
  33. 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.
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Citations

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Cited by:
  1. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2011. "The Merit of High-Frequency Data in Portfolio Allocation," SFB 649 Discussion Papers SFB649DP2011-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Kevin Sheppard, 2014. "Factor High-Frequency Based Volatility (HEAVY) Models," Economics Series Working Papers 710, University of Oxford, Department of Economics.
  3. Bannouh, K. & Martens, M.P.E. & Oomen, R.C.A. & van Dijk, D.J.C., 2012. "Realized mixed-frequency factor models for vast dimensional covariance estimation," ERIM Report Series Research in Management, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasm ERS-2012-017-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  4. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Banco de Espa�a Working Papers 1230, Banco de Espa�a.

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