Nonlinear multiscale coupling analysis of financial time series based on composite complexity synchronization

In the paper, based on the combination of sample entropy and complexity-invariant distance, a new synchrony-measured method, called the composite complexity synchronization (CCS), is proposed to measure the degree of synchrony of two time series with same data length. Implementing the multiscale cross-sample entropy and multiscale composite complexity synchronization (MCCS) analysis for seven representative stock market indexes, multiscale coupling behaviors of logarithmic returns are compared. Furthermore, the selective data of different sampling frequency within the same time period are applied to analyze the effect of sampling rate in the data on the MCCS behaviors. And we apply the ensemble empirical mode decomposition to decompose the stock logarithmic returns into the intrinsic mode functions and investigate the extent that they have inherited the coupling behaviors of original returns. Empirical results demonstrate the feasibility and effectiveness of the proposed method, and exhibit its superiority in distinguishing the very subtle synchrony behaviors among the time series.