Phase and multifractality analyses of random price time series by finite-range interacting biased voter system

A random financial price process which is developed by mechanisms of finite-range interacting biased voter model is considered in the present paper. Voter model is one of statistical physics systems as well as a continuous time Markov process, which originally represents a voter's attitude on a particular topic, namely, voters reconsider their opinions at times distributed according to independent exponential random variables. The empirical mode decomposition method is employed to analyze the behaviors of logarithmic returns for the simulation data of the model and the two real market indexes, Shanghai Composite Index and Deutscher Aktien Index. The multifractal characteristics of the original returns and first 3 intrinsic mode functions (IMFs) after empirical mode decomposition are explored by the multifractal detrended function analysis. The instantaneous phase, amplitude probability distribution of first 4 IMFs, and the multifractal properties of instantaneous amplitude are investigated.