Abstract
The analysis of complex systems frequently poses the challenge to distinguish correlation from causation. Statistical physics has inspired very promising approaches to search for correlations in time series; the transfer entropy in particular (Hlavackova-Schindler et al., 2007). Now, methods from computational statistics can quantitatively assign significance to such correlation measures. In this study, we propose and apply a procedure to statistically assess transfer entropies by one-sided tests. We introduce to null models of vanishing correlations for time series with memory. We implemented them in an OpenMP-based, parallelized C++ package for multi-core CPUs. Using template meta-programming, we enable a compromise between memory and run time efficiency.
Highlights
Natural science strives to find correlations in empirical data to identify patterns that might indicate the presence of causation
Transfer entropy (TE) is – like the related mutual information or other schemes of information theory [22] – efficiently computable whenever the sampling space consists of a set of discrete symbols and in low dimensions, that is with a short history window and makes it an interesting analysis approach to correlated data
While transfer entropy (TE) is a relative entropy, it was shown [11] that it is closely related to the notion of Granger causality
Summary
Natural science strives to find correlations in empirical data to identify patterns that might indicate the presence of causation. Besides the conceptual advantages of the TE, current approaches of using TE [4, 5] face two major problems which we address in this work: (a) computation of the TE can be done directly using simple arrays for the data, but only inefficiently so, and, (b) while we can use the asymmetry TE(X → Y) = TE(Y → X) to guess on the direction of information flow, the TE itself does not allow for a statistical assessment of the significance of such flows and their respective directions We briefly review the TE and general information theory and
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