Detecting direct causality in multivariate time series: A comparative study

TL;DR

This paper compares various causality measures in multivariate time series, demonstrating that dimension reduction techniques outperform others, especially in high-dimensional systems with noise and limited data.

Contribution

It provides a comprehensive evaluation of causality measures, emphasizing the effectiveness of dimension reduction methods in high-dimensional multivariate time series analysis.

Findings

Dimension reduction causality measures outperform others in high-dimensional systems.

Robustness of measures varies with time series length and noise type.

High-dimensional coupled systems benefit from dimension reduction techniques.

Abstract

The concept of Granger causality is increasingly being applied for the characterization of directional interactions in different applications. A multivariate framework for estimating Granger causality is essential in order to account for all the available information from multivariate time series. However, the inclusion of non-informative or non-significant variables creates estimation problems related to the 'curse of dimensionality'. To deal with this issue, direct causality measures using variable selection and dimension reduction techniques have been introduced. In this comparative work, the performance of an ensemble of bivariate and multivariate causality measures in the time domain is assessed, focusing on dimension reduction causality measures. In particular, different types of high-dimensional coupled discrete systems are used (involving up to 100 variables) and the robustness of the causality measures to time series length and different noise types is examined. The results of the simulation study highlight the superiority of the dimension reduction measures, especially for high-dimensional systems.