Scaling, self-similarity and multifractality in FX markets

Zhaoxia Xu, Ramazan Gençay

Research output: Contribution to journalArticlepeer-review


This paper presents an empirical investigation of scaling and multifractal properties of US Dollar-Deutschemark (USD-DEM) returns. The data set is ten years of 5-min returns. The cumulative return distributions of positive and negative tails at different time intervals are linear in the double logarithmic space. This presents strong evidence that the USD-DEM returns exhibit power-law scaling in the tails. To test the multifractal properties of USD-DEM returns, the mean moment of the absolute returns as a function of time intervals is plotted for different powers of absolute returns. These moments show different slopes for these powers of absolute returns. The nonlinearity of the scaling exponent indicates that the returns are multifractal.

Original languageEnglish (US)
Pages (from-to)578-590
Number of pages13
JournalPhysica A: Statistical Mechanics and its Applications
StatePublished - May 15 2003


  • Foreign exchange markets
  • High-frequency data
  • Multifractality
  • Scaling
  • Self-similarity

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics


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