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Bootstrapping realized multivariate volatility measures

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  • Dovonon, Prosper
  • Goncalves, Silvia
  • Meddahi, Nour

Abstract

We study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations. For these measures of covariation, the Monte Carlo simulation results of Barndorff-Nielsen and Shephard (2004) show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent. This motivates our use of the bootstrap as an alternative tool of inference for covariation measures. We consider an i.i.d. bootstrap applied to the vector of returns. We show that the finite sample performance of the bootstrap is superior to the existing first-order asymptotic theory. Nevertheless, and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term, the Edgeworth expansion for the i.i.d. bootstrap that we develop here shows that this method is not second order accurate. We argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility.

Suggested Citation

  • Dovonon, Prosper & Goncalves, Silvia & Meddahi, Nour, 2010. "Bootstrapping realized multivariate volatility measures," MPRA Paper 40123, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:40123
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    References listed on IDEAS

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    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
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    5. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    6. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    7. 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.
    8. 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.
    9. 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.
    10. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    11. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
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    16. Griffin, Jim E. & Oomen, Roel C.A., 2011. "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 58-68, January.
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    18. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    19. Viceira, Luis M., 2012. "Bond risk, bond return volatility, and the term structure of interest rates," International Journal of Forecasting, Elsevier, vol. 28(1), pages 97-117.
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    Citations

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    Cited by:

    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. 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.
    3. 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).
    4. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    5. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    6. Patton, Andrew J. & Verardo, Michela, 2009. "Does beta move with news?: Systematic risk and firm-specific information flows," LSE Research Online Documents on Economics 24421, London School of Economics and Political Science, LSE Library.
    7. 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.
    8. Matteo Bonato & Luca Taschini, 2016. "Comovement and the financialization of commodities," GRI Working Papers 215, Grantham Research Institute on Climate Change and the Environment.
    9. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2014. "Large Deviations Of The Realized (Co-)Volatility Vector," Working Papers hal-01082903, HAL.
    10. Ulrich Hounyo, 2014. "Bootstrapping integrated covariance matrix estimators in noisy jump-diffusion models with non-synchronous trading," CREATES Research Papers 2014-35, Department of Economics and Business Economics, Aarhus University.
    11. repec:eee:spapps:v:127:y:2017:i:9:p:2926-2960 is not listed on IDEAS
    12. Mykland, Per A. & Zhang, Lan, 2016. "Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price," Journal of Econometrics, Elsevier, vol. 194(2), pages 242-262.
    13. repec:eee:econom:v:201:y:2017:i:2:p:417-432 is not listed on IDEAS
    14. Hwang, Eunju & Shin, Dong Wan, 2013. "Stationary bootstrapping realized volatility," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2045-2051.
    15. Vincenzo Candila, 2013. "A Comparison Of The Forecasting Performances Of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    16. Hacène Djellout & Arnaud Guillin & Yacouba Samoura, 2017. "Large Deviations Of The Realized (Co-)Volatility Vector," Post-Print hal-01082903, HAL.
    17. Ulrich Hounyo, 2013. "Bootstrapping realized volatility and realized beta under a local Gaussianity assumption," CREATES Research Papers 2013-30, Department of Economics and Business Economics, Aarhus University.
    18. repec:eee:econom:v:202:y:2018:i:2:p:178-195 is not listed on IDEAS
    19. Hwang, Eunju & Shin, Dong Wan, 2014. "A bootstrap test for jumps in financial economics," Economics Letters, Elsevier, vol. 125(1), pages 74-78.

    More about this item

    Keywords

    Realized regression; realized beta; realized correlation; bootstrap; Edgeworth expansions;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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