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Time Deformation: Definition and Comparisons

Author

Listed:
  • Gaëlle Le Fol

    (DRM - Dauphine Recherches en Management - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Mercier Ludovic

Abstract

In this paper, we are dealing with financial high frequency data; any time an order reaches the market, any time a cancellation or transaction occurs, a new record is made, ending up with a huge amount of data. Hence the time interval between two events is not fixed, forbidding the use of standard statistical tools. In the recent literature, several authors proposed time deformation techniques to deal with this problem. The practical importance of time deformation is to give a preprocessing technique to obtain a regularly spaced grid of data. The main contribution of this paper is to survey most of the time deformations proposed in the literature in a general setting and to compare them from both a statistical and financial point of view. We provide a new trading strategy in which the time to invest is endogeneous. Moreover, we highlight the fact that changing time scale can improve the daily gain following such a strategy.

Suggested Citation

  • Gaëlle Le Fol & Mercier Ludovic, 1998. "Time Deformation: Definition and Comparisons," Post-Print halshs-00586097, HAL.
    • Handle: RePEc:hal:journl:halshs-00586097
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    Citations

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    Cited by:

    1. Antonio A. F. Santos, 2021. "Bayesian Estimation for High-Frequency Volatility Models in a Time Deformed Framework," Computational Economics, Springer;Society for Computational Economics, vol. 57(2), pages 455-479, February.
    2. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    3. Bialkowski, Jedrzej & Darolles, Serge & Le Fol, Gaëlle, 2008. "Improving VWAP strategies: A dynamic volume approach," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1709-1722, September.
    4. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    5. Gunther Capelle-Blancard & Séverine Vandelanoite, 2002. "Relations intrajournalières entre l'indice CAC 40 et les options sur indice : Quel est le marché préféré des investisseurs informés ?," Annals of Economics and Statistics, GENES, issue 66, pages 143-177.
    6. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Gunther Capelle-Blancard & Séverine Vandelanoite, 2000. "Intraday relations between CAC 40 cash index and CAC 40 index options [Relations intrajournalières entre l'indice CAC 40 et les options sur indice. Quel est le marché préféré des investisseurs info," Post-Print halshs-03727911, HAL.
    8. GIOT, Pierre, 1999. "Time transformations, intraday data and volatility models," LIDAM Discussion Papers CORE 1999044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. D. Guegan & L. Mercier, 2005. "Prediction in chaotic time series: methods and comparisons with an application to financial intra-day data," The European Journal of Finance, Taylor & Francis Journals, vol. 11(2), pages 137-150.

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