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Self-affine variation in fractal time

  • Howard M. Taylor
  • Peter K. Clark
Chapter

Abstract

Since the number of transactions in any time period is random, different distributions are needed to represent price changes over fixed numbers of transactions and fixed time periods. It appears that the former follow a Gaussian distribution, while the latter follow a L-stable distribution. M & Taylor 1967 shows that those two distributions are by no means contratictory: a scenario based on a fractal subordination time is proposed by Taylor (Section 1), then shown by Mandelbrot (Section 2) to be intimately related to an earlier discussion of the specialists’ function of “ensuring the continuity of the market.” Note that this scenario is only compatible with the M 1963 model restricted to a symmetric distribution of price changes. Section 3 — reproducing M 1973c — elaborates by responding to Clark 1973.

Keywords

Stock Price Price Change Fractal Time Infinite Variance Sample Moment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Howard M. Taylor
  • Peter K. Clark

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