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Range-Based Estimation of Quadratic Variation

Author

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  • Christensen, Kim
  • Podolskij, Mark

Abstract

This paper proposes using realized range-based estimators to draw inference about the quadratic variation of jump-diffusion processes. We also construct a range-based test of the hypothesis that an asset price has a continuous sample path. Simulated data shows that our approach is efficient, the test is well-sized and more powerful than a return-based t-statistic for sampling frequencies normally used in empirical work. Applied to equity data, we show that the intensity of the jump process is not as high as previously reported.

Suggested Citation

  • Christensen, Kim & Podolskij, Mark, 2006. "Range-Based Estimation of Quadratic Variation," Technical Reports 2006,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    • Handle: RePEc:zbw:sfb475:200637
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Christensen, Kim & Oomen, Roel & Podolskij, Mark, 2010. "Realised quantile-based estimation of the integrated variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 74-98, November.
    2. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. 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.
    4. Neil Shephard & Kevin Sheppard, 2012. "Efficient and feasible inference for the components of financial variation using blocked multipower variation," Economics Series Working Papers 593, University of Oxford, Department of Economics.
    5. Mark Podolskij & Daniel Ziggel, 2007. "A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models," CREATES Research Papers 2007-26, Department of Economics and Business Economics, Aarhus University.
    6. repec:hal:journl:peer-00732538 is not listed on IDEAS
    7. 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.
    8. 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.
    9. 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.
    10. Tseng Tseng-Chan & Chung Huimin & Huang Chin-Sheng, 2009. "Modeling Jump and Continuous Components in the Volatility of Oil Futures," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-30, May.
    11. Giovanni Bonaccolto & Massimiliano Caporin, 2016. "The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective," JRFM, MDPI, vol. 9(3), pages 1-25, July.
    12. Kinnebrock, Silja & Podolskij, Mark, 2008. "A note on the central limit theorem for bipower variation of general functions," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 1056-1070, June.
    13. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    14. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    15. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    16. Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Oxford University Press, vol. 8(1), pages 29-56, Winter.
    17. 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.
    18. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
    19. Tseng, Tseng-Chan & Lee, Chien-Chiang & Chen, Mei-Ping, 2015. "Volatility forecast of country ETF: The sequential information arrival hypothesis," Economic Modelling, Elsevier, vol. 47(C), pages 228-234.
    20. Christensen, Kim & Podolski, Mark, 2005. "Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale," Technical Reports 2005,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    21. Kim Christensen & Mark Podolskij & Mathias Vetter, 2009. "Bias-correcting the realized range-based variance in the presence of market microstructure noise," Finance and Stochastics, Springer, vol. 13(2), pages 239-268, April.
    22. Tseng-Chan Tseng & Hung-Cheng Lai & Cha-Fei Lin, 2012. "The impact of overnight returns on realized volatility," Applied Financial Economics, Taylor & Francis Journals, vol. 22(5), pages 357-364, March.
    23. 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.

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    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
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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