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An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory

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  • Markus Bibinger
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    Abstract

    The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed Itô processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator including a feasible central limit theorem with optimal convergence rate on convenient regularity assumptions. The inevitably remaining impact of asynchronous deterministic sampling schemes and noise corruption on the asymptotic distribution is precisely elucidated. A case study for various important examples, several generalizations of the model and an algorithm for the implementation warrant the utility of the estimation method in applications.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2011-034.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 SFB649DP2011-034.

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    Length: 39 pages
    Date of creation: Jun 2011
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2011-034

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    Related research

    Keywords: non-synchronous observations; microstructure noise; integrated covolatility; multiscale estimator; stable limit theorem;

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    1. 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.
    2. Xiaoliang Liu & Wei Xu & Martin Odening, 2011. "Can crop yield risk be globally diversified?," SFB 649 Discussion Papers SFB649DP2011-018, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Juliane Scheffel, 2011. "Identifying the Effect of Temporal Work Flexibility on Parental Time with Children," SFB 649 Discussion Papers SFB649DP2011-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Dirk Hofmann & Salmai Qari, 2011. "The Law of Attraction: Bilateral Search and Horizontal Heterogeneity," SFB 649 Discussion Papers SFB649DP2011-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Esra Akdeniz Duran & Wolfgang Karl Härdle & Maria Osipenko, 2011. "Difference based Ridge and Liu type Estimators in Semiparametric Regression Models," SFB 649 Discussion Papers SFB649DP2011-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Gunda-Alexandra Detmers & Dieter Nautz, 2011. "The information content of central bank interest rate projections: Evidence from New Zealand," SFB 649 Discussion Papers SFB649DP2011-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Michael C. Burda & Jennifer Hunt, 2011. "What Explains the German Labor Market Miracle in the Great Recession?," SFB 649 Discussion Papers SFB649DP2011-031, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Juliane Scheffel, 2011. "How do Unusual Working Schedules Affect Social Life?," SFB 649 Discussion Papers SFB649DP2011-025, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Beresford, Alastair R. & Kübler, Dorothea & Preibusch, Sören, 2012. "Unwillingness to pay for privacy: A field experiment," Economics Letters, Elsevier, vol. 117(1), pages 25-27.
    10. Johanna Kappus & Markus Reiß, 2010. "Estimation of the characteristics of a Lévy process observed at arbitrary frequency," SFB 649 Discussion Papers SFB649DP2010-015, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Strohsal, Till & Weber, Enzo, 2010. "Mean-Variance Cointegration and the Expectations Hypothesis," University of Regensburg Working Papers in Business, Economics and Management Information Systems 442, University of Regensburg, Department of Economics.
    12. Esra Akdeniz Duran & Mengmeng Guo & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Expectile Functions," SFB 649 Discussion Papers SFB649DP2011-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Shuzhuan Zheng & Lijian Yang & Wolfgang Karl Härdle, 2011. "A Confidence Corridor for Sparse Longitudinal Data Curves," SFB 649 Discussion Papers SFB649DP2011-002, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Wolfgang Karl Härdle & Vladimir Spokoiny & Weining Wang, 2011. "Local Quantile Regression," SFB 649 Discussion Papers SFB649DP2011-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Wolfgang Karl Härdle & Maria Osipenko, 2011. "Spatial Risk Premium on Weather Derivatives and Hedging Weather Exposure in Electricity," SFB 649 Discussion Papers SFB649DP2011-013, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    16. Mechtenberg, Lydia & Münster, Johannes, 2010. "A strategic mediator who is biased into the same direction as the expert can improve information transmission," Discussion Papers, Research Unit: Market Behavior SP II 2010-19, Social Science Research Center Berlin (WZB).
    17. Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2013. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 619-631, June.
    18. Alexander Meyer-Gohde, 2011. "Sticky Information and Determinacy," SFB 649 Discussion Papers SFB649DP2011-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    19. 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.
    20. Lu Lin & Feng Li & Lixing Zhu & Wolfgang Karl Härdle, 2011. "Mean Volatility Regressions," SFB 649 Discussion Papers SFB649DP2011-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    21. Wolfgang Karl Härdle & Brenda López Cabrera & Ostap Okhrin & Weining Wang, 2011. "Localising temperature risk," SFB 649 Discussion Papers SFB649DP2011-001, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    22. Sigbert Klinke, 2011. "Developing web-based tools for the teaching of statistics: Our Wikis and the German Wikipedia," SFB 649 Discussion Papers SFB649DP2011-030, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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