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

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  • Bibinger, Markus

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.

Suggested Citation

  • 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.
    • Handle: RePEc:zbw:sfb649:sfb649dp2011-034
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    References listed on IDEAS

    as
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    14. Awartani, Basel & Corradi, Valentina & Distaso, Walter, 2009. "Assessing Market Microstructure Effects via Realized Volatility Measures with an Application to the Dow Jones Industrial Average Stocks," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 251-265.
    15. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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