Non-parametric Analysis of Granger Causality Using Local Measures of Divergence

The employment of Granger causality analysis on temporal data is now a standard routine in many scientific disciplines. Since its inception, Granger causality has been modeled using a wide variety of analytical frameworks of which, linear models and derivations thereof have been the dominant choice. Nevertheless, a body of research on Granger causality and its applications has focused on non-linear and non-parametric models. One common choice for such models is based on employment of multivariate density estimators and measures of divergence. However, these models are subject to a number of estimations and tuning components that have a great impact on the final outcome. Here we focus on one such general model and improve a number of its tuning bodies. Crucially, we i) investigate the bandwidth selection issue in kernel density estimation, and ii) discuss and propose a solution to the sensitivity of estimated information theoretic measures of divergence to non-linear correspondence. The resulting framework of analysis is evaluated using varied series of simulations.