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Asymptotic theory of range-based multipower variation

Author

Listed:
  • 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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    Citations

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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. Vortelinos, Dimitrios I., 2016. "Incremental information of stock indicators," International Review of Economics & Finance, Elsevier, vol. 41(C), pages 79-97.
    3. Ma, Feng & Liu, Jing & Huang, Dengshi & Chen, Wang, 2017. "Forecasting the oil futures price volatility: A new approach," Economic Modelling, Elsevier, vol. 64(C), pages 560-566.
    4. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2016. "Volatility Jumps and Their Economic Determinants," Journal of Financial Econometrics, Oxford University Press, vol. 14(1), pages 29-80.
    5. Beatriz Vaz de Melo Mendes & Victor Bello Accioly, 2017. "Improving (E)GARCH forecasts with robust realized range measures: Evidence from international markets," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 41(4), pages 631-658, October.
    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. Liu, Qiang & Liu, Yiqi & Liu, Zhi & Wang, Li, 2018. "Estimation of spot volatility with superposed noisy data," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 62-79.
    8. Liao, Yin & Anderson, Heather M., 2019. "Testing for cojumps in high-frequency financial data: An approach based on first-high-low-last prices," Journal of Banking & Finance, Elsevier, vol. 99(C), pages 252-274.
    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.
    10. Gong, Xu & Lin, Boqiang, 2018. "Structural changes and out-of-sample prediction of realized range-based variance in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 27-39.
    11. 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.
    12. Ma, Feng & Zhang, Yaojie & Huang, Dengshi & Lai, Xiaodong, 2018. "Forecasting oil futures price volatility: New evidence from realized range-based volatility," Energy Economics, Elsevier, vol. 75(C), pages 400-409.
    13. Ma, Feng & Li, Yu & Liu, Li & Zhang, Yaojie, 2018. "Are low-frequency data really uninformative? A forecasting combination perspective," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 92-108.
    14. Xu, Yanyan & Huang, Dengshi & Ma, Feng & Qiao, Gaoxiu, 2019. "Liquidity and realized range-based volatility forecasting: Evidence from China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1102-1113.

    More about this item

    Keywords

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

    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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