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Bootstrap Inference for Pre-averaged Realized Volatility based on Nonoverlapping Returns

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  • Sílvia Gonçalves
  • Ulrich Hounyo
  • Nour Meddahi

Abstract

The main contribution of this article 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 nonoverlapping blocks of consecutive observations. Pre-averaging reduces the influence of the noise and allows for realized volatility estimation on the pre-averaged returns. The nonoverlapping nature of the pre-averaged returns implies that these are asymptotically uncorrelated, 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, 2014. "Bootstrap Inference for Pre-averaged Realized Volatility based on Nonoverlapping Returns," Journal of Financial Econometrics, Oxford University Press, vol. 12(4), pages 679-707.
    • Handle: RePEc:oup:jfinec:v:12:y:2014:i:4:p:679-707.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbu011
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    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Francis X. Diebold & Georg Strasser, 2013. "On the Correlation Structure of Microstructure Noise: A Financial Economic Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1304-1337.
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    2. Hwang, Eunju & Shin, Dong Wan, 2018. "Two-stage stationary bootstrapping for bivariate average realized volatility matrix under market microstructure noise and asynchronicity," Journal of Econometrics, Elsevier, vol. 202(2), pages 178-195.
    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, 2017. "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. Podolskij, Mark & Veliyev, Bezirgen & Yoshida, Nakahiro, 2017. "Edgeworth expansion for the pre-averaging estimator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3558-3595.
    6. Meng, Bo & Vijh, Anand M., 2021. "Stock merger activity and industry performance," Journal of Banking & Finance, Elsevier, vol. 129(C).

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    JEL classification:

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

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