Modelling Loss of Complexity in Intermittent Time Series and its Application

In this paper, we developed a novel method of nonparametric relative entropy (RlEn) for modelling loss of complexity in intermittent time series. The method consists of two steps. We first fit a nonlinear autoregressive model to each intermittent time series, where the corresponding lag order and the loss of complexity are determined by Bayesian Information Criterion (BIC) and relative entropy respectively. Then, change-points in the complexity are detected by a cumulative sum (CUSUM) based statistic. Compared to approximate entropy (ApEn), a popular method in literature, the performance of RlEn was assessed by simulations in terms of (1) ability to localize complexity change-points in intermittent time series; (2) ability to faithfully estimate underlying nonlinear models. The performance of the proposal was then examined in a real analysis of fatigue-induced changes in the complexity of human motor outputs. The results showed that the proposed method outperformed the ApEn in accurately detecting changes of complexity in intermittent time series segments.