Multifractal analysis of agent-based financial markets

Abstract

To analyze financial time series exhibiting volatility clustering, long-range dependence, or heavy-tailed marginals, we exploit multifractal analysis and agent-based simulation. We develop a robust, automated software tool for extracting the multifractal spectrum of a time series based on multifractal detrended fluctuation analysis (MF-DFA). The software is tested on simulated data with closed-form monofractal and multifractal spectra to ensure the quality of our implementation. We perform an in-depth analysis of General Electric's stock price using traditional time series techniques, and contrast the results with those obtained using MF-DFA. We also present a zero-intelligence agent-based financial market model and analyze its output using MF-DFA. We study the changes in the macrolevel time series output as analyzed by MF-DFA when altering one of the microlevel agent behaviors. Finally we explore the potential for validating agent-based models against empirical time series using MF-DFA.