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Activity signature functions for high-frequency data analysis

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  • Todorov, Viktor
  • Tauchen, George
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    Abstract

    We 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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    File URL: http://www.sciencedirect.com/science/article/B6VC0-4WW2SRB-2/2/6d25ee3e53b36100ec62c1c90e2e0c31
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 154 (2010)
    Issue (Month): 2 (February)
    Pages: 125-138

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    Handle: RePEc:eee:econom:v:154:y:2010:i:2:p:125-138

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Activity index Blumenthal-Getoor index Jumps Levy process Realized power variation;

    References

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    1. 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.
    2. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    3. 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.
    4. 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.
    5. 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.
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    Cited by:
    1. 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.
    2. Tim Bollerslev & Viktor Todorov, 2010. "Estimation of Jump Tails," Working Papers 10-37, Duke University, Department of Economics.
    3. 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.
    4. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    5. 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.
    6. 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.
    7. Benoît Sévi & César Baena, 2011. "Brownian motion vs. pure-jump processes for individual stocks," Economics Bulletin, AccessEcon, vol. 31(4), pages 3138-3152.

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