On the jump activity index for semimartingales
AbstractEmpirical 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 166 (2012)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom
Semimartingale; Power variation; High frequency; Jump activity index; Stable convergence;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Neil Shephard & Ole Barndorff-Nielsen, 2003.
"Econometrics of testing for jumps in financial economics using bipower variation,"
Economics Series Working Papers
2004-FE-01, University of Oxford, Department of Economics.
- 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.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometrics of testing for jumps in financial economics using bipower variationÂ ," OFRC Working Papers Series 2004fe01, Oxford Financial Research Centre.
- 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.
- 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.
- Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 327-344, December.
- 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.
- Yacine Ait-Sahalia, 2001.
"Telling from Discrete Data Whether the Underlying Continuous-Time Model is a Diffusion,"
NBER Working Papers
8504, National Bureau of Economic Research, Inc.
- 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.
- 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.
- 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.
- Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.