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On Thermodynamic Interpretation of Transfer Entropy
Entropy 2013, 15(3), 767-788; doi:10.3390/e15030767

Transfer Entropy for Coupled Autoregressive Processes

1 Torch Technologies, Inc. Huntsville, AL 35802, USA 2 Army, Redstone Arsenal, Huntsville, AL 35898, USA
* Author to whom correspondence should be addressed.
Received: 26 January 2013 / Revised: 13 February 2013 / Accepted: 19 February 2013 / Published: 25 February 2013
(This article belongs to the Special Issue Transfer Entropy)
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A method is shown for computing transfer entropy over multiple time lags for coupled autoregressive processes using formulas for the differential entropy of multivariate Gaussian processes. Two examples are provided: (1) a first-order filtered noise process whose state is measured with additive noise, and (2) two first-order coupled processes each of which is driven by white process noise. We found that, for the first example, increasing the first-order AR coefficient while keeping the correlation coefficient between filtered and measured process fixed, transfer entropy increased since the entropy of the measured process was itself increased. For the second example, the minimum correlation coefficient occurs when the process noise variances match. It was seen that matching of these variances results in minimum information flow, expressed as the sum of transfer entropies in both directions. Without a match, the transfer entropy is larger in the direction away from the process having the larger process noise. Fixing the process noise variances, transfer entropies in both directions increase with the coupling strength. Finally, we note that the method can be generally employed to compute other information theoretic quantities as well.
Keywords: transfer entropy; autoregressive process; Gaussian process; information transfer transfer entropy; autoregressive process; Gaussian process; information transfer
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hahs, D.W.; Pethel, S.D. Transfer Entropy for Coupled Autoregressive Processes. Entropy 2013, 15, 767-788.

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