Abstract
Transfer entropy is a frequently employed measure of conditional co-dependence in non-parametric analysis of Granger causality. In this paper, we derive analytical expressions for transfer entropy for the multivariate exponential, logistic, Pareto (type I – IV) and Burr distributions. The latter two fall into the class of fat-tailed distributions with power law properties, used frequently in biological, physical and actuarial sciences. We discover that the transfer entropy expressions for all four distributions are identical and depend merely on the multivariate distribution parameter and the number of distribution dimensions. Moreover, we find that in all four cases the transfer entropies are given by the same decreasing function of distribution dimensionality.
Highlights
Granger causality is a well-known concept based on dynamic co-dependence [1]
We will derive the expression for transfer entropy for the multivariate exponential distribution
The focus of this paper has been on non-parametric modeling of Granger causality using transfer entropy
Summary
Granger causality is a well-known concept based on dynamic co-dependence [1]. In the framework of Granger causality, the cause precedes and contains unique information about the effect. The concept of Granger causality has been applied in a wide array of scientific disciplines from econometrics to neurophysiology, from sociology to climate research (see [2,3] and references therein), and most recently in cell biology [4]. In the area of Granger causality, transfer entropy [7], an information theoretical measure of co-dependence based on Shannon entropy, has been applied extensively in non-parametric analysis of time-resolved causal relationships. It has been shown that (conditional) mutual information measured in nats and transfer entropy coincide in definition [8,9,10]
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