The causality measure of partial mutual information from mixed embedding (PMIME) revisited.

The measure of partial mutual information from mixed embedding (PMIME) is an information theory-based measure to accurately identify the direct and directional coupling, termed Granger causality or simply causality, between the observed variables or subsystems of a high-dimensional dynamical and complex system, without any a priori assumptions about the nature of the coupling relationship. In its core, it is a forward selection procedure that aims to iteratively identify the lag-dependence structure of a given observed variable (response) to all the other observed variables (candidate drivers). This model-free approach is capable of detecting nonlinear interactions, abundantly present in real-world complex systems, and it was shown to perform well on multivariate time series of moderately high dimension.

Detecting Nonlinear Interactions in Complex Systems: Application in Financial Markets.

Emerging or diminishing nonlinear interactions in the evolution of a complex system may signal a possible structural change in its underlying mechanism. This type of structural break may exist in many applications, such as in climate and finance, and standard methods for change-point detection may not be sensitive to it. In this article, we present a novel scheme for detecting structural breaks through the occurrence or vanishing of nonlinear causal relationships in a complex system.