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Asymptotic theory of range-based multipower variation

Author

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  • Kim Christensen

    () (Aarhus University and CREATES)

  • Mark Podolskij

    () (University of Heidelberg and CREATES)

Abstract

In this paper, we present a realised range-based multipower variation theory, which can be used to estimate return variation and draw jump-robust inference about the diffusive volatility component, when a high-frequency record of asset prices is available. The standard range-statistic – routinely used in financial economics to estimate the variance of securities prices – is shown to be biased when the price process contains jumps. We outline how the new theory can be applied to remove this bias by constructing a hybrid range-based estimator. Our asymptotic theory also reveals that when high-frequency data are sparsely sampled, as is often done in practice due to the presence of microstructure noise, the range-based multipower variations can produce significant efficiency gains over comparable subsampled returnbased estimators. The analysis is supported by a simulation study and we illustrate the practical use of our framework on some recent TAQ equity data.

Suggested Citation

  • Kim Christensen & Mark Podolskij, 2011. "Asymptotic theory of range-based multipower variation," CREATES Research Papers 2011-47, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-47
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    File URL: ftp://ftp.econ.au.dk/creates/rp/11/rp11_47.pdf
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    Cited by:

    1. Vortelinos, Dimitrios I., 2014. "Optimally sampled realized range-based volatility estimators," Research in International Business and Finance, Elsevier, vol. 30(C), pages 34-50.
    2. repec:oup:jfinec:v:14:y:2016:i:1:p:29-80. is not listed on IDEAS
    3. Duembgen, Moritz & Podolskij, Mark, 2015. "High-frequency asymptotics for path-dependent functionals of Itô semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1195-1217.
    4. repec:spr:jecfin:v:41:y:2017:i:4:d:10.1007_s12197-017-9386-x is not listed on IDEAS
    5. Vortelinos, Dimitrios I., 2016. "Incremental information of stock indicators," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 79-97.
    6. Liu, Jing & Wei, Yu & Ma, Feng & Wahab, M.I.M., 2017. "Forecasting the realized range-based volatility using dynamic model averaging approach," Economic Modelling, Elsevier, vol. 61(C), pages 12-26.
    7. repec:eee:ecmode:v:64:y:2017:i:c:p:560-566 is not listed on IDEAS
    8. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2016. "Volatility Jumps and Their Economic Determinants," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 14(1), pages 29-80.
    9. Zhi Liu, 2017. "Jump-robust estimation of volatility with simultaneous presence of microstructure noise and multiple observations," Finance and Stochastics, Springer, vol. 21(2), pages 427-469, April.

    More about this item

    Keywords

    High-frequency data; Integrated variance; Realised multipower variation; Realised range-basedmultipower variation; Quadratic variation.;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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