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Efficient and feasible inference for the components of financial variation using blocked multipower variation

Author

Listed:
  • Per A. Mykland

    () (Department of Statistics, University of Chicago, USA)

  • Neil Shephard

    () (Nuffield College, Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

  • Kevin Sheppard

    () (Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

Abstract

High frequency financial data allows us to learn more about volatility, volatility of volatility and jumps. One of the key techniques developed in the literature in recent years has been bipower variation and its multipower extension, which estimates time-varying volatility robustly to jumps. We improve the scope and efficiency of multipower variation by the use of a more sophisticated exploitation of high frequency data. This suggests very significant improvements in the power of jump tests. It also yields efficient estimates of the integrated variance of the continuous part of a semimartingale. The paper also shows how to extend the theory to the case where there is microstructure in the observations and derive the first nonparametric high frequency estimator of the volatility of volatility. A fundamental device in the paper is a new type of result showing path-by-path (strong) approximation between multipower and the (unobserved) RV based on the continuous part of the process.

Suggested Citation

  • Per A. Mykland & Neil Shephard & Kevin Sheppard, 2012. "Efficient and feasible inference for the components of financial variation using blocked multipower variation," Economics Papers 2012-W02, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1202
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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2012/mss120221.pdf
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    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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    4. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
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    10. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
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    Citations

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    Cited by:

    1. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
    2. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    3. Markus Bibinger & Per A. Mykland, 2016. "Inference for Multi-dimensional High-frequency Data with an Application to Conditional Independence Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1078-1102, December.
    4. 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.
    5. Yoann Potiron & Per Mykland, 2016. "Local Parametric Estimation in High Frequency Data," Papers 1603.05700, arXiv.org, revised Mar 2017.
    6. Markus Bibinger & Per A. Mykland, 2013. "Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing," SFB 649 Discussion Papers SFB649DP2013-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    7. Jacod, Jean & Klüppelberg, Claudia & Müller, Gernot, 2017. "Testing for non-correlation between price and volatility jumps," Journal of Econometrics, Elsevier, vol. 197(2), pages 284-297.
    8. Simon Clinet & Yoann Potiron, 2017. "Estimation for high-frequency data under parametric market microstructure noise," Papers 1712.01479, arXiv.org.
    9. Mykland, Per A. & Zhang, Lan, 2016. "Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price," Journal of Econometrics, Elsevier, vol. 194(2), pages 242-262.

    More about this item

    Keywords

    bipower variation; jumps; market microstructure noise; multipower variation; nonparametric analysis; quadratic variation; semimartingale; volatility; volatility of volatility.;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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