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

Author

Listed:
  • 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.

Suggested Citation

  • Sílvia Gonçalves & Ulrich Hounyo & Nour Meddahi, 2013. "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns," CREATES Research Papers 2013-07, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2013-07
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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, vol. 159(1), pages 116-133, November.
    10. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
    11. 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.
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    Cited by:

    1. repec:eee:econom:v:202:y:2018:i:2:p:178-195 is not listed on IDEAS
    2. Hounyo, Ulrich & Gonçalves, Sílvia & Meddahi, Nour, 2017. "Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise," Econometric Theory, Cambridge University Press, vol. 33(04), pages 791-838, August.
    3. 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.
    4. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 0509. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    5. repec:eee:spapps:v:127:y:2017:i:11:p:3558-3595 is not listed on IDEAS

    More about this item

    Keywords

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

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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