A model-free causality measure based on multi-variate delay embedding

Abstract

We further delay embedding framework application to multiple time series for extraction of their potential causal interactions. We introduce a novel geometric model-free causality measure that can efficiently detect linear and nonlinear causal interactions between time series with no prior information or parameter estimation. Using multivariate delay embedding, we construct a point cloud from a set of time domain signals and propose the inverse of its fractal dimension as a causal interaction measure between the corresponding time series. Correlation dimension estimation is fully exploited as a fractal-based method for uncovering the dimensions of generated point clouds. Extensive simulation results are presented to substantiate the capabilities of the proposed approach.