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Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice

Author

Listed:
  • Laurent Callot

    (VU University Amsterdam, the Netherlands)

  • Anders B. Kock

    (Aarhus University, Denmark)

  • Marcelo C. Medeiros

    (Pontifical Catholic University of Rio de Janeiro, Brasil)

Abstract

In this paper we consider modeling and forecasting of large realized covariance matrices by penalized vector autoregressive models. We propose using Lasso-type estimators to reduce the dimensionality to a manageable one and provide strong theoretical performance guarantees on the forecast capability of our procedure. To be precise, we show that we can forecast future realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics for the realized covariance matrices of the 30 Dow Jones stocks and find that these dynamics are not stable as the data is aggregated from the daily to the weekly and monthly frequency. The theoretical performance guarantees on our forecasts are illustrated on the Dow Jones index. In particular, we can beat our benchmark by a wide margin at the longer forecast horizons. Finally, we investigate the economic value of our forecasts in a portfolio selection exercise and find that in certain cases an investor is willing to pay a considerable amount in order get access to our forecasts.

Suggested Citation

  • Laurent Callot & Anders B. Kock & Marcelo C. Medeiros, 2014. "Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice," Tinbergen Institute Discussion Papers 14-147/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20140147
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    References listed on IDEAS

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    1. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    2. Jianqing Fan & Yingying Li & Ke Yu, 2012. "Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 412-428, March.
    3. 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.
    4. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2015. "Do High‐Frequency Data Improve High‐Dimensional Portfolio Allocations?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 263-290, March.
    5. Francesco Audrino & Simon D. Knaus, 2016. "Lassoing the HAR Model: A Model Selection Perspective on Realized Volatility Dynamics," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1485-1521, December.
    6. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
    7. 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.
    8. 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.
    9. Jushan Bai & Shuzhong Shi, 2011. "Estimating High Dimensional Covariance Matrices and its Applications," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 199-215, November.
    10. 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.
    11. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    12. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    13. Bauer, Gregory H. & Vorkink, Keith, 2011. "Forecasting multivariate realized stock market volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 93-101, January.
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    Citations

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    Cited by:

    1. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "l1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations," Textos para discussão 636, Department of Economics PUC-Rio (Brazil).
    2. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.

    More about this item

    Keywords

    Realized covariance; vector autoregression; shrinkage; Lasso; forecasting; portfolio allocation;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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