Transfer mutual information: A new method for measuring information transfer to the interactions of time series

In this paper, we propose a new method to measure the influence of a third variable on the interactions of two variables. The method called transfer mutual information (TMI) is defined by the difference between the mutual information and the partial mutual information. It is established on the assumption that if the presence or the absence of one variable does make change to the interactions of another two variables, then quantifying this change is supposed to be the influence from this variable to those two variables. Moreover, a normalized TMI and other derivatives of the TMI are introduced as well. The empirical analysis including the simulations as well as real-world applications is investigated to examine this measure and to reveal more information among variables.