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Bootstrapping realized volatility and realized beta under a local Gaussianity assumption

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  • Ulrich Hounyo

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    (Oxford-Man Institute of Quantitative Finance and CREATES)

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    Abstract

    The main contribution of this paper is to propose a new bootstrap method for statistics based on high frequency returns. The new method exploits the local Gaussianity and the local constancy of volatility of high frequency returns, two assumptions that can simplify inference in the high frequency context, as recently explained by Mykland and Zhang (2009). Our main contributions are as follows. First, we show that the local Gaussian bootstrap is firstorder consistent when used to estimate the distributions of realized volatility and ealized betas. Second, we show that the local Gaussian bootstrap matches accurately the first four cumulants of realized volatility, implying that this method provides third-order refinements. This is in contrast with the wild bootstrap of Gonçalves and Meddahi (2009), which is only second-order correct. Third, we show that the local Gaussian bootstrap is able to provide second-order refinements for the realized beta, which is also an improvement of the existing bootstrap results in Dovonon, Gonçalves and Meddahi (2013) (where the pairs bootstrap was shown not to be second-order correct under general stochastic volatility). Lastly, we provide Monte Carlo simulations and use empirical data to compare the finite sample accuracy of our new bootstrap confidence intervals for integrated volatility and integrated beta with the existing results.

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    File URL: ftp://ftp.econ.au.dk/creates/rp/13/rp13_30.pdf
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    Bibliographic Info

    Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2013-30.

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    Length: 47
    Date of creation: 09 2013
    Date of revision:
    Handle: RePEc:aah:create:2013-30

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    Web page: http://www.econ.au.dk/afn/

    Related research

    Keywords: High frequency data; realized volatility; realized beta; bootstrap; Edgeworth expansions;

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    References

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    1. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, 09.
    2. 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.
    3. 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.
    4. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
    5. Dovonon, Prosper & Goncalves, Silvia & Meddahi, Nour, 2010. "Bootstrapping realized multivariate volatility measures," MPRA Paper 40123, University Library of Munich, Germany.
    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, 05.
    7. 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.
    8. Per A. Mykland & Lan Zhang, 2011. "The Double Gaussian Approximation for High Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 38(2), pages 215-236, 06.
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
    10. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
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