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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.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2011-028.pdf
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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-028.

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Length: 37 pages
Date of creation: May 2011
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2011-028

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Related research

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

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Cited by:
  1. Raffaele Fiocco & Carlo Scarpa, 2011. "The Regulation of Interdependent Markets," SFB 649 Discussion Papers SFB649DP2011-046, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  6. Alexander Meyer-Gohde, 2011. "Monetary Policy, Determinacy, and the Natural Rate Hypothesis," SFB 649 Discussion Papers SFB649DP2011-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  7. Markus Bibinger, 2011. "Asymptotics of Asynchronicity," SFB 649 Discussion Papers SFB649DP2011-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Raffaele Fiocco & Mario Gilli, 2011. "Bargaining and Collusion in a Regulatory Model," SFB 649 Discussion Papers SFB649DP2011-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  9. Ulrich Bindseil & Philipp Johann König, 2011. "The economics of TARGET2 balances," SFB 649 Discussion Papers SFB649DP2011-035, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. 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.
  11. 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.
  12. 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.

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