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Time-Space Scaling of Financial Time Series

  • Yoshiaki Kumagai
Conference paper

Summary

We propose a new method to describe scaling behavior of time series. We introduce an extension of extreme values: maximum and minimum. By using these extreme values determined by time-space scaling with a spread (or width), functions of this spread are defined. One is the number of these extreme values, and the other is the total variation among these extreme values. These functions are independent of time scale. In high frequency data, observations can occur at varying time intervals. In particular, on fractal analysis, interpolation influences the results. Using these functions, we can analyze non-equidistant data without interpolation. Moreover the problem of choosing the appropriate time scale to use for analyzing market data is avoided. In other words, ’time’ is defined by fluctuations here. Lastly, these functions are related to a viewpoint of investor whose transaction costs coincide with the spread.

Key Words

Non-equidistant data Transaction costs Tick-by-tick Fractal Scaling 

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References

  1. 1.
    Clark P K (1973) Subordinated Stochastic Process Model with Finite Variance for Speculative Prices. Econometrica 41: 135–155MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Kumagai Y (1999) Speculative Market Model with Transaction Costs and En-dogenous Horizons . Mita Business Rev (in Japanese) Mita Syougaku Kenkyuu 42, 4: 71–92Google Scholar
  3. 3.
    Kumagai Y (2000) Analysis of Trading Volume and Liquidity by Speculative Market Model with Transaction Costs and Endogenous Horizons (in Japanese)Google Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Yoshiaki Kumagai
    • 1
  1. 1.Institute for Economic and Industrial StudiesKeio UniversityMinato-ku, TokyoJapan

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