The novel multi-scale local irreversibility analysis method based on segmentation about time series

Abstract

In this paper, we mainly study the local irreversibility of time series. For this purpose, inspired by the idea of segmentation contained in multi-fractal detrended fluctuation analysis, we propose a novel time series irreversibility analysis, that is, multi-scale local irreversibility method based on the segmentation. By means of this method, we can availably discuss the fluctuation of local irreversibility of a time series as the timescale changes. In order to explore the performance of this method in analyzing the local irreversibility of time series in depth, we provide the definition of Kullback–Leibler distribution (KLD) combined with the horizontal visibility graph algorithm, which has been verified to be an intuitive method for the analysis of irreversibility. Meanwhile, we also introduce three other irreversible indices: Porta’s, Guzik’s and Ehler’s indices ($$P\%$$, $$G\%$$ and E, respectively) for deeper detection. Further on, we first apply the above methods to the simulated time series generated by the auto-regressive fractionally integrated moving average model and financial time series. By virtue of the new multi-scale local irreversibility analysis method, the results show that KLD and Ehler’s index are superior to the other two measures when comparing the difference of local irreversibility of different time series. At the same time, we also find an interesting phenomenon, that is, results of Porta’s index are similar to those of Guzik’s index and both of them can better expose the similarity of local irreversibility of different time series. Besides, all of them can exhibit their powerful function in analyzing the relationship of the holistic and local irreversibility of a time series. As a further validation, we specially examine effect of the new method on the analysis to different electrocardiogram signals. The results provide us with plenty of meaningful results, which are consequential for disease detection.