Interacting price model and fluctuation behavior analysis from Lempel-Ziv complexity and multi-scale weighted-permutation entropy

A financial price model is developed based on the voter interacting system in this work. The Lempel-Ziv complexity is introduced to analyze the complex behaviors of the stock market. Some stock market stylized facts including fat tails, absence of autocorrelation and volatility clustering are investigated for the proposed price model firstly. Then the complexity of fluctuation behaviors of the real stock markets and the proposed price model are mainly explored by Lempel-Ziv complexity (LZC) analysis and multi-scale weighted-permutation entropy (MWPE) analysis. A series of LZC analyses of the returns and the absolute returns of daily closing prices and moving average prices are performed. Moreover, the complexity of the returns, the absolute returns and their corresponding intrinsic mode functions (IMFs) derived from the empirical mode decomposition (EMD) with MWPE is also investigated. The numerical empirical study shows similar statistical and complex behaviors between the proposed price model and the real stock markets, which exhibits that the proposed model is feasible to some extent.