  Information theoretic measures (entropies, entropy rates, mutual information)
are nowadays commonly used in statistical signal processing for real-world data
analysis. The present work proposes the use of Auto Mutual Information (Mutual
Information between subsets of the same signal) and entropy rate as powerful
tools to assess refined dependencies of any order in signal temporal dynamics.
Notably, it is shown how two-point Auto Mutual Information and entropy rate
unveil information conveyed by higher order statistic and thus capture details
of temporal dynamics that are overlooked by the (two-point) correlation
function. Statistical performance of relevant estimators for Auto Mutual
Information and entropy rate are studied numerically, by means of Monte Carlo
simulations, as functions of sample size, dependence structures and hyper
parameters that enter their definition. Further, it is shown how Auto Mutual
Information permits to discriminate between several different non Gaussian
processes, having exactly the same marginal distribution and covariance
function. Assessing higher order statistics via multipoint Auto Mutual
Information is also shown to unveil the global dependence structure fo these
processes, indicating that one of the non Gaussian actually has temporal
dynamics that ressembles that of a Gaussian process with same covariance while
the other does not.
