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Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise

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  • Reiß, Markus

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 .... As an application, simple rateoptimal estimators of the volatility and efficient estimators of the integrated volatility are constructed.

Suggested Citation

  • Reiß, Markus, 2011. "Asymptotic equivalence and sufficiency for volatility estimation under microstructure noise," SFB 649 Discussion Papers 2011-028, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2011-028
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    Cited by:

    1. 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.
    2. repec:hum:wpaper:sfb649dp2011-046 is not listed on IDEAS
    3. Stahlschmidt, Stephan & Tausendteufel, Helmut & Härdle, Wolfgang Karl, 2011. "Bayesian Networks and sex-related homicides," SFB 649 Discussion Papers 2011-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. repec:hum:wpaper:sfb649dp2011-042 is not listed on IDEAS
    5. Fiocco, Raffaele & Scarpa, Carlo, 2011. "The regulation of interdependent markets," SFB 649 Discussion Papers 2011-046, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    6. repec:hum:wpaper:sfb649dp2011-034 is not listed on IDEAS
    7. Moreno-Bromberg, Santiago & Taschini, Luca, 2011. "Pollution permits, strategic trading and dynamic technology adoption," LSE Research Online Documents on Economics 37581, London School of Economics and Political Science, LSE Library.
    8. Bindseil, Ulrich & König, Philipp Johann, 2011. "The economics of TARGET2 balances," SFB 649 Discussion Papers 2011-035, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. repec:hum:wpaper:sfb649dp2011-049 is not listed on IDEAS
    10. repec:hum:wpaper:sfb649dp2011-045 is not listed on IDEAS
    11. repec:hum:wpaper:sfb649dp2011-047 is not listed on IDEAS
    12. repec:hum:wpaper:sfb649dp2011-035 is not listed on IDEAS
    13. Raffaele Fiocco & Mario Gilli, 2012. "Bargaining and Collusion in a Regulatory Model," Chapters, in: Joseph E. Harrington Jr & Yannis Katsoulacos (ed.), Recent Advances in the Analysis of Competition Policy and Regulation, chapter 12, Edward Elgar Publishing.
    14. Reiß, Markus & Rozenholc, Yves & Cuenod, Charles A., 2011. "Pointwise adaptive estimation for quantile regression," SFB 649 Discussion Papers 2011-029, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. repec:hum:wpaper:sfb649dp2011-043 is not listed on IDEAS
    16. Naujokat, Felix & Horst, Ulrich, 2011. "When to cross the spread: Curve following with singular control," SFB 649 Discussion Papers 2011-053, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    17. repec:hum:wpaper:sfb649dp2011-053 is not listed on IDEAS
    18. repec:hum:wpaper:sfb649dp2011-029 is not listed on IDEAS
    19. repec:hum:wpaper:sfb649dp2011-033 is not listed on IDEAS
    20. Bibinger, Markus, 2011. "Asymptotics of asynchronicity," SFB 649 Discussion Papers 2011-033, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    21. Bibinger, Markus, 2011. "An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory," SFB 649 Discussion Papers 2011-034, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    22. Meyer-Gohde, Alexander, 2011. "Monetary policy, determinacy, and the natural rate hypothesis," SFB 649 Discussion Papers 2011-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    23. repec:hum:wpaper:sfb649dp2011-052 is not listed on IDEAS
    24. Moreno-Bromberg, Santiago & Pirvu, Traian A. & Réveillac, Anthony, 2011. "CRRA utility maximization under risk constraints," SFB 649 Discussion Papers 2011-043, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.

    More about this item

    Keywords

    high-frequency data; integrated volatility; spot volatility estimation; Le Cam deficiency; equivalence of experiments; Gaussian shift;
    All these keywords.

    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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