I have two time-series U and V (approximately 300 samples) having values between 0 and 5. I wanted to calculate the (first order) transfer entropy $I_{uv}$ (of U with the knowledge of V) and $I_{vu}$ (of V with the knowledge of U). Here are the values I got :

$I_{uv}$ = 0.1492 and $I_{vu}$ = 0.1342

Since these values are close to each other, I started questioning their significance. Thus, I calculated the transfer entropy $I_{u-rv}$ of U with the knowledge of a randomized (in time) version of V, and the transfer entropy $I_{v-ru}$ of V with the knowledge of a randomized (in time) version of U. I calculated 500 values of $I_{u-rv}$ and $I_{v-ru}$, which gave me :

mean($I_{u-rv}$ ) = 0.1218 - standard deviation = 0.0198

mean($I_{v-ru}$) = 0.1019 - standard deviation = 0.0198

The values of $I_{uv}$ and $I_{vu}$ lie close to (mean+std) so I would say there is an influence of one time serie on the other. From these information what can really be said about the two time-series ? (I will upload a picture of these time-series as soon as I figure a way to do it)


1 Answer 1


You are certainly addressing the problem in the correct manner: creating surrogate "source" time series by randomising/shuffling (while leaving the "destination" unchanged), then computing TE for each surrogate, so as to obtain the distribution of surrogate TEs that one would see were there no source-destination relationship (while other aspects of the time-series are controlled). You can then make a statistical comparison of your measured TE to this distribution so as to check if there is a statistically significant source-destination relationship.

This approach is described formally in the following papers:

  • Chavez et. al., "Statistical assessment of nonlinear causality: application to epileptic EEG signals", Journal of Neuroscience Methods 124 (2003) 113-128.
  • Verdes, P.F., "Assessing causality from multivariate time series", Phys. Rev. E 72(2), 026222–9 (2005)
  • Vicente et al., "Transfer entropy—a model-free measure of effective connectivity for the neurosciences", Journal of Computational Neuroscience, Vol. 30, No. 1. (2011), pp. 45-67
  • Lizier et al., "Multivariate information-theoretic measures reveal directed information structure and task relevant changes in fMRI connectivity", Journal of Computational Neuroscience, Vol. 30, No. 1. (2011), pp. 85-107.

Assuming your surrogate distribution followed a normal distribution, you could do Student's t-test for significance of the measured values; while their p-values are high, neither is statistically significant at alpha=0.05; I would say that you don't have a statistically significant relationship there.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.