Statistical Property of Price Fluctuations in a Multi-Agent Model and the Currency Exchange Market
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We show that the price fluctuation generated in a multi-agent model of economic system driven by the positive feedback mechanism exhibits nonGaussioan (Lévy) statistics of various range of parameter α, from the Cauchy distribution (α=1) to the Gauss distribution (α=2).
Two different patterns are observed in the time series of price fluctuation, one of which is characterized by the intermittency and its probability distribution corresponds to the Cauchy distribution, and the other pattern corresponds to the Gauss distribution, within a range of 0.01 < a,b < 0.1, where a is the price denomination rate, and b is the price inflation constant assumed in the model. The former pattern occurs in the region of a<b (‘bull’ market situation), and the latter in the region of a>b ( ‘bear’ market situation). The boundary of the two phases roughly corresponds to a line a = b where the price patterns show a certain critical behavior and its probability distribution roughly fits Lévy distribution of α =1.7.
We compare this result to the real-world data. The fact that the short term currency exchange data (JPY/USD) per trade for the duration of ten days in 1998 fits the Lévy distribution of α=1.7 very well indicates that the data corresponds to the moderate market in which the price denomination rate a and the price inflation constant b are roughly equal in our model.
Key wordsPositive feedback Mechanism Lévy distribution Intermittency Anti Oscillation Cooperative Phenomena
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- Bachelier L (1900) Théorie de la speculation. Doctor Thesis. Annales Scientifiques de l’Ecole Normale Sperieure III-17:21–86; Translation (1964) P.H. Cootner(Ed.) the Random character of stock market prices, MIT Press, pp 17–18Google Scholar
- Tanaka-Yamawaki M (2000) A Study of Chaotic and Non-chaotic Phase Structure in the Positive Feedback Model of Trading Agents. Tokuyama M, Stanley HE (eds) Statistical Physics, pp 692–698Google Scholar
- Tanaka-Yamawaki M (2001) Information 4:179–185Google Scholar
- Sato AH, Takayasu H (2001) In this ProceedingsGoogle Scholar
- Tanaka-Yamawaki M, Kitamaru Y (2000) Technical Report of IEICE: NLP99–156 (in Japanese) 47–52Google Scholar
- Kitamaru Y (2000) Senior Thesis submitted to Miyazaki UniversityGoogle Scholar
- Tanaka-Yamawaki M, Ohta T (2001) Memoirs of Faculty of Engineering, Miyazaki UniversityGoogle Scholar
- Ohta T (2001) Seior Thesis submitted to Miyazaki UniversityGoogle Scholar
- Tanaka-Yamawaki M (2000) Proceedings of 5th Joint Conference on Information Sciences 2:965–967Google Scholar
- Tanaka-Yamawaki M, Hasebe K, Jain LC (1995) Proceedings of ETD2000. IEEE Computer Society Press Los Alamos CA USA, pp 571–577Google Scholar
- Tanaka-Yamawaki M, Tabuse M (1999) Periodic Motion After Chaos in a Model of Trading Agents. Proceedings of the fourth Symposium on Artificial Life and Robotics, pp 548–551Google Scholar
- Tanaka-Yamawaki M, Tabuse M (1998) Chaotic Structure in an Artificial Economic System. Proceedings of 5th International Conference on Soft Computing and Information/Intelligent Systems, World Scientific, pp 884–887Google Scholar
- Tanaka-Yamawaki M, Tabuse M (1997) Chaotic Time Series from a Model of trading Agents. Proceedings of Int. Conf. Nonlinear Theory and Applications, pp 285–288Google Scholar
- Yanagawa K (1998) Ms. Thesis submitted to Nihon UniversityGoogle Scholar