Chaoticity and Fractality Analysis of an Artificial Stock Market Generated by the Multi-Agent Systems Based on the Co-evolutionary Genetic Programming

摘要

This paper deals with the chaoticity and fractality analysis of price time series for artificial stock market generated by the multi-agent systems based on the co-evolutionary Genetic Programming (GP). By simulation studies, if the system parameters and the system construction are appropriately chosen, the system shows very monotonic behaviors or sometime chaotic time series. Therefore, it is necessary to show the relationship between the realizability (reproducibility) of the system and the system parameters. This paper describe the relation between the chaoticity of an artificial stock price and system parameters. We also show the condition for the fractality of a stock price. Although the Chaos and the Fractal are the signal which can be obtained from the system which is generally different, we show that those can be obtained from a single system. Cognitive behaviors of agents are modeled by using the GP to introduce social learning as well as individual learning. Assuming five types of agents, in which rational agents prefer forecast models (equations) or production rules to support their decision making, and irrational agents select decisions at random like a speculator. Rational agents usually use their own knowledge base, but some of them utilize their public (common) knowledge base to improve trading decisions. By assuming that agents with random behavior are excluded and each agent uses the forecast model or production rule with most highest fitness, those assumptions are derived a kind of chaoticity from stock price. It is also seen that the stock price becomes fractal time series if we utilize original framework for the multi-agent system and relax the restriction of systems for chaoticity.