Measuring time series based on multiscale dispersion Lempel–Ziv complexity and dispersion entropy plane

Abstract

Abstract In this paper, we propose dispersion Lempel–Ziv complexity and combine it with dispersion entropy to construct complexity-entropy plane. This measure aims to identify time series with different properties. These two quantities take advantage of nonlinear symbolic representation and quantify the complexity of series. In addition, they are relatively stable for different parameters and robust against white noise with different levels. The complexity-entropy plane is able to identify nonlinear chaotic maps and distinguish them from stochastic process. Also, the multiscale features of signals are detected, suggesting the underlying dynamics. This technique is effective to track the dynamical changes of heart rate time series and to characterize different pathologic states. It can also prove that aging and disease correspond to the loss of complexity.