Activity signature functions for high-frequency data analysis
AbstractWe define a new concept termed activity signature function, which is constructed from discrete observations of a continuous-time process, and derive its asymptotic properties as the sampling frequency increases. We show that the function is a useful device for estimating the activity level of the underlying process and in particular for deciding whether the process contains a continuous martingale. An application to $ /DM exchange rate over 1986-1999 indicates that a jump-diffusion model is more plausible than a pure-jump model. A second application to internet traffic at NASA servers shows that an infinite variation pure-jump model is appropriate for its modeling.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 154 (2010)
Issue (Month): 2 (February)
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Web page: http://www.elsevier.com/locate/jeconom
Activity index Blumenthal-Getoor index Jumps Levy process Realized power variation;
Other versions of this item:
- George Tauchen & Viktor Todorov, 2010. "Activity Signature Functions for High-Frequency Data Analysis," Working Papers 10-08, Duke University, Department of Economics.
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- Ballotta, Laura, 2005. "A Lévy process-based framework for the fair valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 173-196, October.
- S. Z. Levendorski, 2004. "Early exercise boundary and option prices in Levy driven models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 525-547.
- 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.
- 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.
- Carr, Peter & Wu, Liuren, 2007.
"Stochastic skew in currency options,"
Journal of Financial Economics,
Elsevier, vol. 86(1), pages 213-247, October.
- Elton A. Daal & Dilip B. Madan, 2005. "An Empirical Examination of the Variance-Gamma Model for Foreign Currency Options," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2121-2152, November.
- Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
- Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
- Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382.
- Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005.
"A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data,"
Journal of the American Statistical Association,
American Statistical Association, vol. 100, pages 1394-1411, December.
- Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
- Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
- Tim Bollerslev & Viktor Todorov, 2010.
"Estimation of Jump Tails,"
10-37, Duke University, Department of Economics.
- Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2011.
"Realized Laplace transforms for estimation of jump diffusive volatility models,"
Journal of Econometrics,
Elsevier, vol. 164(2), pages 367-381, October.
- Viktor Todorov & Iaryna Grynkiv & George Tauchen, 2010. "Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models," Working Papers 10-75, Duke University, Department of Economics.
- Julien Chevallier & Benoît Sévi, 2012. "On the Stochastic Properties of Carbon Futures Prices," Working Papers halshs-00720166, HAL.
- Viktor Todorov & George Tauchen & Iaryna Grynkiv, 2011.
"Volatility Activity: Specification and Estimation,"
11-23, Duke University, Department of Economics.
- Benoît Sévi & César Baena, 2011. "Brownian motion vs. pure-jump processes for individual stocks," Economics Bulletin, AccessEcon, vol. 31(4), pages 3138-3152.
- Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Which continuous-time model is most appropriate for exchange rates?," Working Papers 2013-024, Federal Reserve Bank of St. Louis.
- Torben G. Andersen & Oleg Bondarenko & Viktor Todorov & George Tauchen, 2013. "The Fine Structure of Equity-Index Option Dynamics," CREATES Research Papers 2013-52, School of Economics and Management, University of Aarhus.
- Torben G. Andersen & Oleg Bondarenko & Maria T. Gonzalez-Perez, 2011. "Coherent Model-Free Implied Volatility: A Corridor Fix for High-Frequency VIX," CREATES Research Papers 2011-49, School of Economics and Management, University of Aarhus.
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