Fuzzy entropy complexity and multifractal behavior of statistical physics financial dynamics

Abstract

The present paper introduces a novel stochastic statistical physics financial system by combining exclusion system with compound Poisson process. The financial system is a model concerning with price fluctuations derived from dissemination of trading attitudes of financial agents and random drastic jumps caused by exogenous economic factors, respectively. Multifractal detrended cross-correlation analysis and fuzzy entropy of simulation dataset are performed. Fractional fuzzy entropy based on fuzzy entropy method and fractional calculus, is also developed to explore nonlinear complexity of the proposed model in the paper. Empirical results display that there are significant multifractality and fractal asymmetry in the proposed model, and the complexity of return series increases when λ or γ increases, correspondingly. And same analyses for actual stock market dataset are comparatively investigated. The conclusions reveal that the novel compound dynamics can reproduce various nonlinear behaviors of actual stock markets to a certain extent.