Entropia de transferência para cadeias estocásticas com memória de alcance variável

Abstract

Transfer entropy is a measure of causality between two time series, quantifying the information that one process provides about the future of another. In this thesis, we consider the problem of estimating the transfer entropy rate between two discrete stochastic processes using the plug-in estimator. When the joint process is a stationary, absolutely regular chain with variable-length memory and whose the dynamics is governed by a 𝑔-function that is not necessarily continuous but is perfectly simulatable, we derive bounds for the probability of concentration of the empirical transfer entropy around its mean and its rate. Next, we establish the convergence of this estimator to a normal distribution, thus providing a Central Limit Theorem for this functional. In this case, we restrict our analysis to processes compatible with continuous 𝑔-functions.