Fractality of profit landscapes and validation of time series models for stock prices

  • Il Gu Yi
  • Gabjin Oh
  • Beom Jun Kim
Regular Article


We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters p and q, and the sell (buy) decision is made when the log return is larger (smaller) than p (−q). We discretize the unit square (p,q) ∈ [0,1] × [0,1] into the N × N square grid and the profit Π(p,q) is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: the number M of local maxima follows the power-law form MN a , but the scaling exponent a is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent a ≈ 1.6 observed for real stock markets. We suggest that the fractality of profit landscape characterized by a ≈ 1.6 can be a useful measure to validate time series model for stock prices.


Statistical and Nonlinear Physics 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.BK21 Physics Research Division and Department of PhysicsSungkyunkwan UniversitySuwonKorea
  2. 2.Division of Business AdministrationChosun UniversityGwangjuKorea

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