Nonlinear extensions of new causality

Abstract

New causality (NC) is a relatively recent method for inferring causal relationships between time-series data. Similar to other popular causal inference methods, like Granger causality (GC), NC can be evaluated in time or frequency domain. NC derives its value by partitioning a predictive model, grouping them by different inputs, and finding a normalized ratio of the power of all contributions. In its seminal form, NC is defined atop a linear ARMAX models. If the contribution between two time-series cannot be accurately expressed with a linear model, the seminal form of NC cannot accurately measure the causal relationship. In the frequency domain, linear models also prevent cross-frequency contributions from being measured. This work introduces an extension to NC to NARMAX models. This extension reduces to the seminal form when applied to linear models and can be also evaluated in the frequency domain. The nonlinear extension is applied to a range of synthetic models and real EEG data with promising results. A discussion on modeling and its effect on linear and nonlinear NC estimates is provided.