Abstract
We analyze statistical properties of a random walker in a randomly changing potential function called the PUCK model both theoretically and numerically. In this model the center of the potential function moves with the moving average of the random walker’s trace, and the potential function is given by a quadratic function with its curvature slowly changing around zero. By tuning several parameters the basic statistical properties fit nicely with those of real financial market prices, such as power law price change distribution, very short decay of autocorrelation of price changes, long tails in autocorrelation of the square of price changes and abnormal diffusion in short time scale.
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Acknowledgement
The authors acknowledge Professors Takatoshi Ito and Tsutomu Watanabe for helpful discussions.
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Takayasu, M., Watanabe, K., Mizuno, T., Takayasu, H. (2010). Theoretical Base of the PUCK-Model with Application to Foreign Exchange Markets. In: Takayasu, M., Watanabe, T., Takayasu, H. (eds) Econophysics Approaches to Large-Scale Business Data and Financial Crisis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53853-0_5
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DOI: https://doi.org/10.1007/978-4-431-53853-0_5
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-53852-3
Online ISBN: 978-4-431-53853-0
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