This study faces the problem of causal inference in multivariate dynamic processes, with specific regard to the detection of instantaneous and time-lagged directed interactions. We point out the limitations of the traditional Granger causality analysis, showing that it leads to false detection of causality when instantaneous and time-lagged effects coexist in the process structure. Then, we propose an improved algorithm for causal inference that combines the Granger framework with the approach proposed by Pearl for the study of causality among multiple random variables. This new approach is compared with the traditional one in theoretical and simulated examples of interacting processes, showing its ability to retrieve the correct structure of instantaneous and time-lagged interactions. These approaches for causal inference are then tested on the physiological variability series of heart period, arterial pressure and cerebral blood flow variability obtained in subjects with postural-related syncope during a tilt-test protocol.
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