Evaluation of missing ordinal pattern and its fractional distribution entropy

Abstract

The number of missing ordinal patterns (NMP) receives extensive attention. In this paper, we change the perspective and study NMP about time delay and multi-scale theory. We first highlight the surrogate framework to see if the NMP for a series is statistically different from that of iterative amplitude adjusted Fourier transform (IAAFT) surrogates as time delay and scales changes. Furthermore, by means of the fractional calculus, we combine NMP with distribution entropy to study the fractional distribution entropy with NMP. In order to show the advantages of these methods, several simulated data and electrocardiograph (ECG) signals are chosen to examine the performance of them. Through experiments, we find that NMP about time delay and multi-scale theory shows an excellent characteristic in the nonlinearity analysis of different time series, especially when applied to ECG signals. Moreover, the results of the fractional distribution entropy show that it can explore the complexity of dynamical systems effectively.