Summary
International Symposium on Nonlinear Theory and its Applications
2009
Session Number:B3L-D
Session:
Number:B3L-D4
Estimation of Models and Parameter in Generation Processes of Multi-fractal Signals based on the Multi-Agent Systems
Yoshikazu Ikeda, Shozo Tokinaga,
pp.-
Publication Date:2009/10/18
Online ISSN:2188-5079
Summary:
This paper deals with the estimation of models and parameters in generation processes of multi-fractal signals (time series) based on the multi-agent systems. In the model for multi-fractal time series, cognitive behaviors of agents are modeled by using the GP for learning. As a result, we find strict multi-fractality in artificial stock prices, and we see the relationship between the realizability (reproducibility) of multi-fractality and the system parameters. Features derived from the multi-fractality based on the wavelet transform are used as the input to the conventional discriminant analysis so as to identify the behaviors of agents. However, generally we need sufficient samples to estimate the Hausdorff dimension D(h). To overcome these difficulties, we extend the method to generate multi-fractal times series based on the Wavelet Transform. As applications, we evaluate the performance of interpolation method of the paper by comparing the result of discriminant analysis of agents’ behavior using Genetic Programming (GP) for learning with sufficient samples, and we also discuss the recognition of generation models of real stock prices.