Augmenting Granger Causality through continuous ordinal patterns

We here propose a novel methodology, based on the concept of continuous ordinal patterns, to preprocess time series and make explicit the non-linear temporal structures in them present. Through a series of synthetic and real-world examples, we show how such transformation overcomes one major limitation of the celebrated Granger Causality test, and allows to efficiently detect non-linear causality relations without the need of a priori assumptions. We further show how such transformation can be optimised based on the time series under study; but that good results can also be achieved using random ordinal patterns, in a way similar to how randomness is exploited in Reservoir Computing. We finally discuss the complementarity between this approach and the standard Granger one, especially in the analysis of real-world, and hence unknown, causal relations.

Automated summary

We propose a novel methodology based on continuous ordinal patterns to preprocess time series and uncover the non-linear temporal structures within them. Through synthetic and real-world examples, we demonstrate how this transformation overcomes a major limitation of the Granger Causality test and efficiently detects non-linear causality relations without any prior assumptions. We also show that this transformation can be optimized based on the specific time series under study, or random ordinal patterns can be used to achieve good results, similar to Reservoir Computing.