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Activity signature functions for high-frequency data analysis

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  • Todorov, Viktor
  • Tauchen, George

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.

Suggested Citation

  • Todorov, Viktor & Tauchen, George, 2010. "Activity signature functions for high-frequency data analysis," Journal of Econometrics, Elsevier, vol. 154(2), pages 125-138, February.
  • Handle: RePEc:eee:econom:v:154:y:2010:i:2:p:125-138
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    Cited by:

    1. Andersen, Torben G. & Bondarenko, Oleg & Todorov, Viktor & Tauchen, George, 2015. "The fine structure of equity-index option dynamics," Journal of Econometrics, Elsevier, vol. 187(2), pages 532-546.
    2. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 0509. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    3. repec:ipg:wpaper:2014-565 is not listed on IDEAS
    4. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    5. repec:eee:spapps:v:127:y:2017:i:7:p:2208-2242 is not listed on IDEAS
    6. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
    7. repec:eee:econom:v:202:y:2018:i:1:p:18-44 is not listed on IDEAS
    8. 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.
    9. Erdemlioglu, Deniz & Laurent, Sébastien & Neely, Christopher J., 2015. "Which continuous-time model is most appropriate for exchange rates?," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 256-268.
    10. Tim Bollerslev & Viktor Todorov, 2011. "Estimation of Jump Tails," Econometrica, Econometric Society, vol. 79(6), pages 1727-1783, November.
    11. repec:eee:econom:v:203:y:2018:i:2:p:256-266 is not listed on IDEAS
    12. 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, Department of Economics and Business Economics, Aarhus University.
    13. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    14. Benoît Sévi & César Baena, 2011. "Brownian motion vs. pure-jump processes for individual stocks," Economics Bulletin, AccessEcon, vol. 31(4), pages 3138-3152.
    15. Yacine Aït-Sahalia & Jean Jacod, 2010. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," NBER Working Papers 15808, National Bureau of Economic Research, Inc.
    16. 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.
    17. Ulrich Hounyo & Rasmus T. Varneskov, 2015. "A Local Stable Bootstrap for Power Variations of Pure-Jump Semimartingales and Activity Index Estimation," CREATES Research Papers 2015-26, Department of Economics and Business Economics, Aarhus University.
    18. 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.
    19. Caporin, Massimiliano & Kolokolov, Aleksey & Renò, Roberto, 2014. "Multi-jumps," MPRA Paper 58175, University Library of Munich, Germany.
    20. repec:eee:econom:v:204:y:2018:i:1:p:18-32 is not listed on IDEAS
    21. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2016. "Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach," CREATES Research Papers 2016-27, Department of Economics and Business Economics, Aarhus University.

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