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Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns

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Author Info

  • Sílvia Gonçalves

    ()
    (Université de Montréal, Département de sciences économiques, CIREQ and CIRANO)

  • Ulrich Hounyo

    ()
    (University of Oxford and CREATES)

  • Nour Meddahi

    ()
    (Toulouse School of Economics)

Abstract

The main contribution of this paper is to propose bootstrap methods for realized volatility-like estimators defined on pre-averaged returns. In particular, we focus on the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009). This statistic can be written (up to a bias correction term) as the (scaled) sum of squared pre-averaged returns, where the pre-averaging is done over all possible non-overlapping blocks of consecutive observations. Pre-averaging reduces the influence of the noise and allows for realized volatility estimation on the pre-averaged returns. The non-overlapping nature of the pre-averaged returns implies that these are asymptotically independent, but possibly heteroskedastic. This motivates the application of the wild bootstrap in this context. We provide a proof of the first order asymptotic validity of this method for percentile and percentile-t intervals. Our Monte Carlo simulations show that the wild bootstrap can improve the finite sample properties of the existing first order asymptotic theory provided we choose the external random variable appropriately. We use empirical work to illustrate its use in practice.

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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 2013-07.

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Length: 22
Date of creation: 02 2013
Date of revision:
Handle: RePEc:aah:create:2013-07

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

Related research

Keywords: High frequency data; realized volatility; pre-averaging; market microstructure noise; wild bootstrap.;

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References

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  1. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre.
  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. 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.
  4. 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.
  5. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
  6. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
  7. Francis X. Diebold & Georg Strasser, 2013. "On the Correlation Structure of Microstructure Noise: A Financial Economic Approach," Review of Economic Studies, Oxford University Press, vol. 80(4), pages 1304-1337.
  8. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
  9. 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.
  10. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  11. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
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