Stochastic Interacting Agent-based Financial Price Complex System And Statistical Analysis

With the economic globalization and the fast development of the financial market-s,the financial markets have become the most active trading markets,so the financial modeling of the financial markets is becoming a key problem in financial fields.In this paper,a voter financial price model is developed by applying the voter interacting sys-tem to model the interaction of the agents of financial markets.The fat tails,absence of autocorrelation and volatility clustering of the simulated data are analysed to ex-plore whether there are some stock market stylized facts in the proposed model firstly.Then,a novel complexity measure called Lempel-Ziv complexity(LZC)is introduced to explore the randomness of the financial markets.A series of complexity and ran-domness analysis of the returns,the absolute returns and their corresponding intrinsic mode functions derived from the empirical mode decomposition are performed with Lempel-Ziv complexity and multi-scale weighted-permutation entropy.Furthermore,the complexity-invariance distance(CID)is applied to study the similarity of the real stock markets and the proposed model.A simple classification of real indexes and the simulated data is obtained according the CID values for each stock pairs.Besides,we propose a new method called auto-CID analysis to study the similarity of the newest data and the historical data of the returns.Finally,a new statistic-volatility difference component is introduced in an attempt to study the volatility behaviors comprehensive-ly.We develop a new method to explore the nonlinear phenomena of volatilities by transferring the volatility series to three kinds of volatility duration statistical series.The Zipf method and the permutation LZC which combines the LZC and a new sym-bolic conversion method called the permutation conversion are applied to investigate the Zipf distributions and the complex random behaviors of the three series.The empirical study shows the 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.