Complexity multiscale asynchrony measure and behavior for interacting financial dynamics

•A financial price dynamical model is developed based on the multitype contact interacting system.•MSE analysis is adopted to study the complexity behaviors of several different shuffled return series.•CMSCE analysis is firstly proposed to investigate the asynchrony of stock market dynamics.•Empirical results show the rationality of the proposed financial model and the CMSCE method.

A stochastic financial price process is proposed and investigated by the finite-range multitype contact dynamical system, in an attempt to study the nonlinear behaviors of real asset markets. The viruses spreading process in a finite-range multitype system is used to imitate the interacting behaviors of diverse investment attitudes in a financial market, and the empirical research on descriptive statistics and autocorrelation behaviors of return time series is performed for different values of propagation rates. Then the multiscale entropy analysis is adopted to study several different shuffled return series, including the original return series, the corresponding reversal series, the random shuffled series, the volatility shuffled series and the Zipf-type shuffled series. Furthermore, we propose and compare the multiscale cross-sample entropy and its modification algorithm called composite multiscale cross-sample entropy. We apply them to study the asynchrony of pairs of time series under different time scales.