Equiprobable symbolization pattern entropy for time series complexity measurement

Abstract

AbstractIn order to effectively mine the structural features in time series and simplify the complexity of time series analysis, equiprobable symbolization pattern entropy (EPSPE) is proposed in this paper. The original time series are implemented through symbolic processing according to an equal probability distribution. Then, the sliding window technique is used to obtain a finite number of different symbolic patterns, and the pattern pairs are determined by calculating the conversion between the symbolic patterns. Next, the conversion frequency between symbolized patterns is counted to calculate the probability of the pattern pairs, thus estimating the complexity measurement of complex signals. Finally, we conduct extensive experiments based on the Logistic system under different parameters and the natural wind field. The experimental results show our EPSPE of the Logistic system increases from 5 to 7.5 as the parameters increase, which makes the distinction of periodic and complex time series with varying degrees intuitive. Meanwhile, it can more concisely reflect the structural characteristics and interrelationships between time series from the natural wind field (8.8–10 for outdoor and 7.8–8.3 for indoor). In contrast, the results of several state-of-the-art schemes are irregular and cannot distinguish the complexity of periodic time series as well as accurately predict the spatial deployment relationship of nine 2D ultrasonic anemometers.