Coupling Analysis in Time Series using Information Theory and Dynamical Systems Theory

Abstract

Inferring causality from observations of different entities is central to science. Time series is an important form of observations in subjects ranging from physics, geology and medicine to finance. Although non-experimental observations such as time series measured from geological entities and financial markets are in general never sufficient for causality inference in the strictest sense, couplings inferred from non-experimental time series are still strong hints for causality. Linear methods such as Granger causality, and nonlinear methods such as transfer entropy, have been developed for coupling inference in binary time series or even multiple time series. Among nonlinear method, there are methods such as Cross Convergent Mapping (CCM) which assumes the process under investigation is deterministic and methods such as transfer entropy in principle can accommodate stochastic processes. In this work, we combine CCM and Holstein’s embedding criterion, a criterion based on information entropy, to create an algorithm that is more sensitive than CCM.