Complex Similarity and Fluctuation Dynamics of Financial Markets on Voter Interacting Dynamic System

Abstract

A financial price dynamics is developed based on the voter interacting system, in an attempt to investigate and reproduce the complex similarity and the fluctuation dynamics of financial markets. The complexity-invariance distance (CID) is applied to study the similarity of each stock pairs. A simple classification of seven real indexes and the simulated data is obtained according to the CID values for each stock pairs. The corresponding multiscale dynamical behaviors of CID values are also studied by combining CID with the multiscale method. Further, the similarity of the newest data and the historical data of the returns is investigated by a novel auto-CID analysis, and a corresponding exponent relationship is exhibited. Moveover, the cross correlation function (CCF) is applied to study the correlation of each stock pairs and the causalities of these stock pairs are investigated by the Granger causality method. Besides, the complexity and the randomness of fluctuations of returns, surrogate returns, shuffled returns and intrinsic mode functions (derived from empirical mode decomposition) are also explored at different thresholds with Lempel–Ziv complexity. The empirical study shows complex similarity and similar random property between the proposed price model and the real stock markets, which exhibits that the proposed model is feasible to some extent.