Methods for Reconstructing Causal Networks from Observed Time-Series: Granger-Causality, Transfer Entropy, and Convergent Cross-Mapping

Objectives and Scope A major question that arises in many areas of Cognitive Science is the need to distinguish true causal connections between variables from mere correlations. The most common way of addressing this distinction is the design of wellcontrolled experiments. However, in many situations, it is extremely difficult –or even outright impossible– to perform such experiments. Researchers are then forced to rely on correlational data in order to make causal inferences. This situation is especially common when one needs to analyze longitudinal data corresponding to historical time-series, symbolic sequences, or developmental data. These inferences are often very problematic. From the correlations alone it is difficult to determine the direction of the causal arrow linking two variables. Worse even, the lack of controls of observational data entail that correlations found between two variables need not reflect any causal connection between them. The possibility always remains that some third variable which the researchers were not able to measure, or were actually unaware of, is the actually driver for both measured variables, giving rise to the mirage of a direct relationship between them. In recent years, it has been shown that, under particular circumstances, one can use correlational information for making sound causal inferences (cf., Pearl, 2000). In this tutorial I will provide a hands-on introduction to the use of modern causality techniques for the analysis of observational time series. I will cover causality analyses for three types of time-series that are often encountered in Cognitive Science research: