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Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method


  • Jacod, Jean
  • Mykland, Per A.


This paper introduces adaptiveness to the non-parametric estimation of volatility in high frequency data. We consider general continuous Itô processes contaminated by microstructure noise. In the context of pre-averaging, we show that this device gives rise to estimators that are within 7% of the commonly conjectured “quasi-lower bound” for asymptotic efficiency. The asymptotic variance is of the form constant × bound, where the constant does not depend on the process to be estimated. The results hold with mild assumptions on the noise, and extend to mildly irregular observations.

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  • Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
  • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:2910-2936
    DOI: 10.1016/

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    References listed on IDEAS

    1. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    2. Randolf Altmeyer & Markus Bibinger, 2014. "Functional stable limit theorems for efficient spectral covolatility estimators," SFB 649 Discussion Papers SFB649DP2014-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    7. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
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    20. Markus Bibinger & Markus Reiß, 2014. "Spectral Estimation of Covolatility from Noisy Observations Using Local Weights," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 23-50, March.
    21. Markus Bibinger & Markus Reiss & Nikolaus Hautsch & Peter Malec, 2014. "Estimating the Spot Covariation of Asset Prices – Statistical Theory and Empirical Evidence," SFB 649 Discussion Papers SFB649DP2014-055, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    22. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274,
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    Cited by:

    1. Altmeyer, Randolf & Bibinger, Markus, 2015. "Functional stable limit theorems for quasi-efficient spectral covolatility estimators," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4556-4600.
    2. repec:eee:econom:v:206:y:2018:i:1:p:103-142 is not listed on IDEAS
    3. Ikeda, Shin S., 2016. "A bias-corrected estimator of the covariation matrix of multiple security prices when both microstructure effects and sampling durations are persistent and endogenous," Journal of Econometrics, Elsevier, vol. 193(1), pages 203-214.


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