https://doi.org/10.1140/epjb/e2013-31116-3
Regular Article
Fractality of profit landscapes and validation of time series models for stock prices
1 BK21 Physics Research Division and Department of Physics, Sungkyunkwan University, 440-746 Suwon, Korea
2 Division of Business Administration, Chosun University, 501-759 Gwangju, Korea
a
e-mail: phecogjoh@chosun.ac.kr
b
e-mail: beomjun@skku.edu
Received: 12 December 2012
Received in final form: 7 June 2013
Published online: 5 August 2013
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 M ∼ Na, 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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013