Compression-Complexity with Ordinal Patterns for Robust Causal Inference in Irregularly-Sampled Time Series

TL;DR

This paper introduces Permutation CCC, a novel causality measure for multidimensional irregularly-sampled time series, enhancing robustness and applicability over previous methods.

Contribution

It proposes an ordinal pattern encoding scheme to extend Compression-Complexity Causality to multidimensional data, enabling analysis of complex systems with hidden variables.

Findings

PCCC performs well on numerical simulations.

It effectively analyzes paleoclimate data.

Retains robustness to irregular sampling and missing data.

Abstract

Distinguishing cause from effect is a scientific challenge resisting solutions from mathematics, statistics, information theory and computer science. Compression-Complexity Causality (CCC) is a recently proposed interventional measure of causality, inspired by Wiener-Granger's idea. It estimates causality based on change in dynamical compression-complexity (or compressibility) of the effect variable, given the cause variable. CCC works with minimal assumptions on given data and is robust to irregular-sampling, missing-data and finite-length effects. However, it only works for one-dimensional time series. We propose an ordinal pattern symbolization scheme to encode multidimensional patterns into one-dimensional symbolic sequences, and thus introduce the Permutation CCC (PCCC), which retains all advantages of the original CCC and can be applied to data from multidimensional systems with potentially hidden variables. PCCC is tested on numerical simulations and applied to paleoclimate data characterized by irregular and uncertain sampling and limited numbers of samples.