Annals of Finance

, Volume 4, Issue 2, pp 217–241

Fractals in trade duration: capturing long-range dependence and heavy tailedness in modeling trade duration

  • Wei Sun
  • Svetlozar Rachev
  • Frank J. Fabozzi
  • Petko S. Kalev
Research Article

DOI: 10.1007/s10436-007-0078-y

Cite this article as:
Sun, W., Rachev, S., Fabozzi, F.J. et al. Annals of Finance (2008) 4: 217. doi:10.1007/s10436-007-0078-y


Several studies that have investigated a few stocks have found that the spacing between consecutive financial transactions (referred to as trade duration) tend to exhibit long-range dependence, heavy tailedness, and clustering. In this study, we empirically investigate whether a larger sample of stocks exhibit those characteristics. We do so by comparing goodness of fit in modeling trade duration data for stable distribution and fractional stable noise based on a procedure applying bootstrap methods developed by the authors with several alternative distributional assumptions in modeling trade duration data. The empirical results suggest that the autoregressive conditional duration model with stable distribution fits better than other combinations, while fractional stable noise itself fits better for the time series of trade duration. Our result is consistent with the general findings in the literature that trade duration is informative and that short trade durations move prices more than long trade duration. In addition, our result confirms the advantage of fractal models in the study of roughness in trade duration and provides some evidence for duration dependence.


Fractal processesPoint processesSelf-SimilarityStable distributionTrade duration

JEL Classification


Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Wei Sun
    • 1
  • Svetlozar Rachev
    • 1
    • 2
  • Frank J. Fabozzi
    • 3
    • 4
  • Petko S. Kalev
    • 5
  1. 1.Institute for Statistics and Mathematical EconomicsUniversity of KarlsruheKarlsruheGermany
  2. 2.Department of Statistics and Applied ProbabilityUniversity of CaliforniaSanta BarbaraUSA
  3. 3.Yale School of ManagementNew HavenUSA
  4. 4.School of ManagementYale UniversityNew HavenUSA
  5. 5.Department of Accounting and FinanceMonash UniversityMelbourneAustralia