STATISTICAL PROPERTIES AND MULTIFRACTAL BEHAVIORS OF MARKET RETURNS BY ISING DYNAMIC SYSTEMS

Wen Fang () and Jun Wang
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Wen Fang: Institute of Financial Mathematics and Financial Engineering, College of Science, Beijing Jiaotong University, Beijing 100044, P. R. China
Jun Wang: Institute of Financial Mathematics and Financial Engineering, College of Science, Beijing Jiaotong University, Beijing 100044, P. R. China

International Journal of Modern Physics C (IJMPC), 2012, vol. 23, issue 03, 1-14

Abstract: An interacting-agent model of speculative activity explaining price formation in financial markets is considered in the present paper, which based on the stochastic Ising model and the mean field theory. The model describes the interaction strength among the agents as well as an external field, and the corresponding random logarithmic price return process is investigated. According to the empirical research of the model, the time series formed by this Ising model exhibits the bursting typical of volatility clustering, the fat-tail phenomenon, the power-law distribution tails and the long-time memory. The statistical properties of the returns of Hushen 300 Index, Shanghai Stock Exchange (SSE) Composite Index and Shenzhen Stock Exchange (SZSE) Component Index are also studied for comparison between the real time series and the simulated ones. Further, the multifractal detrended fluctuation analysis is applied to investigate the time series returns simulated by Ising model have the distribution multifractality as well as the correlation multifractality.

Keywords: Stochastic Ising model; mean field theory; time series; long memory; multifractal detrended fluctuation analysis (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (18)

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DOI: 10.1142/S0129183112500234

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