Connectivity Analysis for Multivariate Time Series: Correlation vs. Causality

The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task. There are two distinct cases of interdependence. In the first case, the variables evolve in synchrony, connections are undirected and the connectivity is examined based on symmetric measures, such as correlation. In the second case, a variable drives another one and they are connected with a causal relationship. Therefore, directed connections entail the determination of the interrelationships based on causality measures. The main open question that arises is the following: can symmetric correlation measures or directional causality measures be applied to infer the connectivity network of an examined system? Using simulations, we demonstrate the performance of different connectivity measures in case of contemporaneous or/and temporal dependencies. Results suggest the sensitivity of correlation measures when temporal dependencies exist in the data. On the other hand, causality measures do not spuriously indicate causal effects when data present only contemporaneous dependencies. Finally, the necessity of introducing effective instantaneous causality measures is highlighted since they are able to handle both contemporaneous and causal effects at the same time. Results based on instantaneous causality measures are promising; however, further investigation is required in order to achieve an overall satisfactory performance.