Causality Detection: An Overview of the Methodologies for Time Series Analysis

Coupling and synchronization are common phenomena that occur in nature, e.g. in biological, physiological and environmental systems, as well as in physics and engineered systems. Lag or intermittent lag synchronization, where the difference between the output of one system and the time-delayed output of a second system are asymptotically bounded, is typical case for characterizing the fusion plasma instability control by pace-making techniques [1-2]. The major issue in determining the efficiency of the pacing techniques resides in the periodic or quasiperiodic nature of the occurrence of plasma instabilities. After the perturbation induced by the control systems, if enough time is allowed to pass, the instabilities are bound to reoccur. Therefore, for evaluating the efficiency triggering capability, it is important determine the appropriate time interval over which the pacing techniques have a real influence. Several independent classes of statistical indicators introduced to address this issue are presented. The transfer entropy [3] is a powerful tool for measuring the causation between dynamical events. The amount of information exchanged between two systems depends not only the magnitude but also the direction of the cause-effect relation. Recurrence plots (RP) is an advanced technique of nonlinear data analysis, revealing all the times when the phase space trajectory of the dynamical system visits roughly the same area in the phase space [4]. Convergent cross mapping (CCM) [5], tests for causation by measuring the extent to which the historical record of one time series values can reliably estimate states of the other time series. CCM searches for the signature of X in Y's time series by detecting whether there is a correspondence between the points in the attractor manifolds built from the two time series. A recently developed method [6] for the characterization of interconnected dynamical systems coupling is also presented. The method is based on the representation of time series as weighted cross-visibility networks. The weights are introduced as the metric distance between connected nodes. The structure of the networks, depending on the coupling strength, is quantified via the entropy of the weighted adjacency matrix.