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Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise

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  • Markus Reiß

Abstract

The basic model for high-frequency data in finance is considered, where an efficient price process is observed under microstructure noise. It is shown that this nonparametric model is in Le Cam's sense asymptotically equivalent to a Gaussian shift experiment in terms of the square root of the volatility function σ. As an application, simple rateoptimal estimators of the volatility and efficient estimators of the integrated volatility are constructed.

Suggested Citation

  • Markus Reiß, 2011. "Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise," SFB 649 Discussion Papers SFB649DP2011-028, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2011-028
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    Cited by:

    1. Raffaele Fiocco & Mario Gilli, 2016. "Bargaining and collusion in a regulatory relationship," Journal of Economics, Springer, vol. 117(2), pages 93-116, March.
    2. Santiago Moreno-Bromberg & Luca Taschini, 2011. "Pollution permits, Strategic Trading and Dynamic Technology Adoption," SFB 649 Discussion Papers SFB649DP2011-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Ulrich Bindseil & Philipp Johann König, 2011. "The economics of TARGET2 balances," SFB 649 Discussion Papers SFB649DP2011-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Fiocco, Raffaele & Scarpa, Carlo, 2014. "The regulation of markets with interdependent demands," Information Economics and Policy, Elsevier, vol. 27(C), pages 1-12.
    5. Raffaele Fiocco & Mario Gilli, 2012. "Bargaining and Collusion in a Regulatory Model," Chapters,in: Recent Advances in the Analysis of Competition Policy and Regulation, chapter 12 Edward Elgar Publishing.
    6. Santiago Moreno-Bromberg & Traian A. Pirvu & Anthony Réveillac, 2011. "CRRA Utility Maximization under Risk Constraints," SFB 649 Discussion Papers SFB649DP2011-043, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Felix Naujokat & Ulrich Horst, 2011. "When to Cross the Spread: Curve Following with Singular Control," SFB 649 Discussion Papers SFB649DP2011-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Markus Reiß & Yves Rozenholc & Charles A. Cuenod, 2011. "Pointwise adaptive estimation for quantile regression," SFB 649 Discussion Papers SFB649DP2011-029, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Markus Bibinger, 2011. "An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory," SFB 649 Discussion Papers SFB649DP2011-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Markus Bibinger, 2011. "Asymptotics of Asynchronicity," SFB 649 Discussion Papers SFB649DP2011-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Anand, Kartik & Gai, Prasanna & Marsili, Matteo, 2012. "Rollover risk, network structure and systemic financial crises," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1088-1100.
    12. Alexander Meyer-Gohde, 2011. "Monetary Policy, Determinacy, and the Natural Rate Hypothesis," SFB 649 Discussion Papers SFB649DP2011-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Stephan Stahlschmidt & Helmut Tausendteufel & Wolfgang K. Härdle, 2011. "Bayesian Networks and Sex-related Homicides," SFB 649 Discussion Papers SFB649DP2011-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    High-frequency data; integrated volatility; spot volatility estimation; Le Cam deficiency; equivalence of experiments; Gaussian shift;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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