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On the jump activity index for semimartingales


  • Jing, Bing-Yi
  • Kong, Xin-Bing
  • Liu, Zhi
  • Mykland, Per


Empirical evidence of asset price discontinuities or “jumps” in financial markets has been well documented in the literature. Recently, Aït-Sahalia and Jacod (2009b) defined a general “jump activity index” to describe the degree of jump activities for asset price semimartingales, and provided a consistent estimator when the underlying process contains both a continuous and a jump component. However, only large increments were used in their estimator so that the effective sample size is very small even for large sample sizes. In this paper, we explore ways to improve the Aït-Sahalia and Jacod estimator by making use of all increments, large and small. The improvement is verified through simulations. A real example is also given.

Suggested Citation

  • Jing, Bing-Yi & Kong, Xin-Bing & Liu, Zhi & Mykland, Per, 2012. "On the jump activity index for semimartingales," Journal of Econometrics, Elsevier, vol. 166(2), pages 213-223.
  • Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:213-223 DOI: 10.1016/j.jeconom.2011.09.036

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    References listed on IDEAS

    1. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    3. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 327-344, December.
    4. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    5. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    6. Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
    7. Viktor Todorov & George Tauchen, 2010. "Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation," Working Papers 10-74, Duke University, Department of Economics.
    8. Yacine Aït-Sahalia, 2002. "Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion," Journal of Finance, American Finance Association, vol. 57(5), pages 2075-2112, October.
    9. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. repec:eee:econom:v:202:y:2018:i:1:p:18-44 is not listed on IDEAS
    2. Hounyo, Ulrich & Varneskov, Rasmus T., 2017. "A local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation," Journal of Econometrics, Elsevier, vol. 198(1), pages 10-28.
    3. Figueroa-López, José E. & Nisen, Jeffrey, 2013. "Optimally thresholded realized power variations for Lévy jump diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2648-2677.
    4. Adam D. Bull, 2014. "Near-optimal estimation of jump activity in semimartingales," Papers 1409.8150,, revised Jan 2016.
    5. 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.
    6. repec:oup:biomet:v:104:y:2017:i:2:p:397-410. is not listed on IDEAS
    7. Torben G. Andersen & Nicola Fusari & Viktor Todorov & Rasmus T. Varneskov, 1001. "Option Panels in Pure-Jump Settings," CREATES Research Papers 2018-04, Department of Economics and Business Economics, Aarhus University.
    8. Xin Zhang & Donggyu Kim & Yazhen Wang, 2016. "Jump Variation Estimation with Noisy High Frequency Financial Data via Wavelets," Econometrics, MDPI, Open Access Journal, vol. 4(3), pages 1-26, August.
    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.


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