IDEAS home Printed from https://ideas.repec.org/p/knz/dpteco/1230.html
   My bibliography  Save this paper

Forecasting Covariance Matrices: A Mixed Frequency Approach

Author

Listed:
  • 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.

Suggested Citation

  • Roxana Halbleib & Valeri Voev, 2012. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Paper Series of the Department of Economics, University of Konstanz 2012-30, Department of Economics, University of Konstanz.
  • Handle: RePEc:knz:dpteco:1230
    as

    Download full text from publisher

    File URL: http://www.uni-konstanz.de/FuF/wiwi/workingpaperseries/WP_Halbleib-Voev_30-12.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, pages 3-27.
    2. Meitz, Mika & Saikkonen, Pentti, 2011. "Parameter Estimation In Nonlinear Ar–Garch Models," Econometric Theory, Cambridge University Press, pages 1236-1278.
    3. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    4. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, pages 1545-1578.
    5. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, pages 619-638.
    6. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, pages 579-625.
    8. Neil Shephard & Kevin Sheppard, 2009. "Realising the future: forecasting with high frequency based volatility (HEAVY) models," Economics Series Working Papers 438, University of Oxford, Department of Economics.
    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. Bauer, Gregory H. & Vorkink, Keith, 2011. "Forecasting multivariate realized stock market volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 93-101, January.
    11. repec:oxf:wpaper:264 is not listed on IDEAS
    12. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, pages 619-638.
    13. Ingmar Nolte & Valeri Voev, 2008. "Estimating High-Frequency Based (Co-) Variances: A Unified Approach," CREATES Research Papers 2008-31, Department of Economics and Business Economics, Aarhus University.
    14. 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, pages 94-108.
    15. 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, Department of Economics and Business Economics, Aarhus University.
    16. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, pages 307-327.
    17. Colacito, Riccardo & Engle, Robert F. & Ghysels, Eric, 2011. "A component model for dynamic correlations," Journal of Econometrics, Elsevier, vol. 164(1), pages 45-59, September.
    18. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    19. Audrino, Francesco & Corsi, Fulvio, 2010. "Modeling tick-by-tick realized correlations," Computational Statistics & Data Analysis, Elsevier, pages 2372-2382.
    20. 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).
    21. Hautsch, Nikolaus & Kyj, Lada M. & Malec, Peter, 2011. "The merit of high-frequency data in portfolio allocation," CFS Working Paper Series 2011/24, Center for Financial Studies (CFS).
    22. Audrino, Francesco & Corsi, Fulvio, 2010. "Modeling tick-by-tick realized correlations," Computational Statistics & Data Analysis, Elsevier, pages 2372-2382.
    23. 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.
    24. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    25. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, "undated". "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, Department of Economics and Business Economics, Aarhus University.
    26. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    27. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    28. 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 1-32, November.
    29. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, pages 116-133.
    30. 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.
    31. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    32. 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.
    33. 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.
    34. 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, September.
    35. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    36. Gregory H. Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    37. Hafner, Christian M. & Reznikova, Olga, 2012. "On the estimation of dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, pages 3533-3545.
    38. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers 2005_2, York University, Department of Economics.
    39. 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 351-362, July.
    40. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    41. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hautsch, Nikolaus & Voigt, Stefan, 2017. "Large-Scale Portfolio Allocation Under Transaction Costs and Model Uncertainty: Adaptive Mixing of High- and Low-Frequency Information," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168222, Verein für Socialpolitik / German Economic Association.
    2. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España;Working Papers Homepage.
    3. Roland Weigand, 2014. "Matrix Box-Cox Models for Multivariate Realized Volatility," Working Papers 144, Bavarian Graduate Program in Economics (BGPE).
    4. Matteo Luciani & David Veredas, "undated". "A simple model for vast panels of volatilities," ULB Institutional Repository 2013/136239, ULB -- Universite Libre de Bruxelles.
    5. repec:cte:wsrepe:es142416 is not listed on IDEAS
    6. 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 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.
    7. Veredas, David & Vander Elst, Harry, 2014. "Disentangled jump-robust realized covariances and correlations with non-synchronous prices," DES - Working Papers. Statistics and Econometrics. WS ws142416, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Kevin Sheppard, 2014. "Factor High-Frequency Based Volatility (HEAVY) Models," Economics Series Working Papers 710, University of Oxford, Department of Economics.
    9. Hautsch, Nikolaus & Kyj, Lada M. & Malec, Peter, 2011. "The merit of high-frequency data in portfolio allocation," CFS Working Paper Series 2011/24, Center for Financial Studies (CFS).
    10. Altavilla, Carlo & Giannone, Domenico & Modugno, Michele, 2017. "Low frequency effects of macroeconomic news on government bond yields," Journal of Monetary Economics, Elsevier, pages 31-46.

    More about this item

    Keywords

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

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:knz:dpteco:1230. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Office Ursprung). General contact details of provider: http://edirc.repec.org/data/fwkonde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.