Abstract
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.
Highlights
The study of the interdependence relationships of the variables of an examined system is of great importance and remains a challenging task
The second simulation system demonstrates the effect of time-lagged directional relationships on the connectivity measures and in particular on correlation measures that are not defined in order to detect lagged dependencies
We have presented a brief review of the main connectivity measures currently used to infer the connectivity network of a examined complex system
Summary
There are various challenges in the analysis of multivariate high-dimensional systems, such as in the analysis of financial and neurophysiological data. Some limitations relevant to causal measures are the sample size bias, the common input problem, the effect of noise and the curse of dimensionality [36,37,38,39,40,41,42]. Selecting between correlation and causality measures for inferring the connectivity structure of an examined system is of the key interest of this study; it is essential to demonstrate the performance and pitfalls of the different connectivity measures focusing on those that have not been stressed and investigated extensively so far. We examine the influence of the existence of contemporaneous interdependencies to the extracted causal network, the effect of causal relationships when forming correlation networks and inquire the case of having both contemporaneous and causal relationships among the variables of a multivariate system
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