Order pattern recurrence for the analysis of complex systems

Abstract

In this paper, order pattern recurrence plot (OPRP) and order pattern recurrence quantification analysis (OPRQA) are proposed to quantify recurrence characteristics of complex systems. The method uses the recurrence of order patterns in symbolic sequence to explore the order structure of the original data, in which the color of the symbol is employed to distinguish different order patterns. The main advantage of the approach is its robustness with respect to non-stationary data and low requirements for the length of the required time series. The method is demonstrated to be effective in synthetic data and real data. As demonstrated in simulation models, the conclusion is that the method can not only make a distinction between chaotic system and random noise but also quantify various bifurcation transition scenarios like period doubling or other phenomena associated with chaos-to-chaos transitions in logistic map. In empirical analysis, this approach helps observe the different performance of the time series before, during and after the financial crisis. In addition, differences of stocks between developing countries and developed countries are reflected in OPRP and quantified by the corresponding OPRQA. The proposed method brings together recurrence plots and symbolic dynamics to empower researchers with effective means to visualize and quantify complex behavior in dynamic system.