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Functional stable limit theorems for efficient spectral covolatility estimators

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  • Randolf Altmeyer
  • Markus Bibinger

Abstract

We consider noisy non-synchronous discrete observations of a continuous semimartingale. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: onedimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. In particular, the derived asymptotic variances coincide with the benchmarks of semiparametric Cram´er-Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized sub-experiments. Feasible central limit theorems allowing for confidence are provided.

Suggested Citation

  • Randolf Altmeyer & Markus Bibinger, 2014. "Functional stable limit theorems for efficient spectral covolatility estimators," SFB 649 Discussion Papers SFB649DP2014-005, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2014-005
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    References listed on IDEAS

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    5. Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2013. "Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency," SFB 649 Discussion Papers SFB649DP2013-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    8. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
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    10. Christensen, Kim & Podolskij, Mark & Vetter, Mathias, 2013. "On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 59-84.
    11. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    12. Markus Bibinger, 2011. "Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 23-45, March.
    13. Clément, Emmanuelle & Delattre, Sylvain & Gloter, Arnaud, 2013. "An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatility," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2500-2521.
    14. Renault, Eric & Sarisoy, Cisil & Werker, Bas J.M., 2017. "Efficient Estimation Of Integrated Volatility And Related Processes," Econometric Theory, Cambridge University Press, vol. 33(2), pages 439-478, April.
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    Cited by:

    1. Markus Bibinger & Nikolaus Hautsch & Peter Malec & Markus Reiss, 2019. "Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 419-435, July.
    2. Jacod, Jean & Mykland, Per A., 2015. "Microstructure noise in the continuous case: Approximate efficiency of the adaptive pre-averaging method," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 2910-2936.
    3. Bibinger, Markus & Winkelmann, Lars, 2015. "Econometrics of co-jumps in high-frequency data with noise," Journal of Econometrics, Elsevier, vol. 184(2), pages 361-378.
    4. Markus Bibinger & Lars Winkelmann, 2014. "Common price and volatility jumps in noisy high-frequency data," SFB 649 Discussion Papers SFB649DP2014-037, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Markus Bibinger & Markus Reiss & Nikolaus Hautsch & Peter Malec, 2014. "Estimating the Spot Covariation of Asset Prices – Statistical Theory and Empirical Evidence," SFB 649 Discussion Papers SFB649DP2014-055, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. Linzert, Tobias & Winkelmann, Lars & Bibinger, Markus, 2014. "ECB monetary policy surprises: identification through cojumps in interest rates," Working Paper Series 1674, European Central Bank.

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    More about this item

    Keywords

    adaptive estimation; asymptotic efficiency; local parametric estimation; microstructure noise; integrated volatility; non-synchronous observations; spectral estimation; stable limit theorem;
    All these keywords.

    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

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