Fractal structure of financial high frequency data

Yoshiaki Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We propose a new method to describe scaling behavior of time series. We introduce an extension of extreme values. Using these extreme values determined by a scale, we define some functions. Moreover, using these functions, we can measure a kind of fractal dimension - fold dimension. In financial high frequency data, observations can occur at varying time intervals. Using these functions, we can analyze non-equidistant data without interpolation or evenly sampling. Further, the problem of choosing the appropriate time scale is avoided. Lastly, these functions are related to a viewpoint of investor whose transaction costs coincide with the spread.

Original languageEnglish
Pages (from-to)13-18
Number of pages6
Issue number1
Publication statusPublished - 2002 Aug 19
Externally publishedYes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Geometry and Topology
  • Applied Mathematics


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