  Multivariate time series analysis is becoming an integral part of data
analysis pipelines. Understanding the individual time point connections between
covariates as well as how these connections change in time is non-trivial. To
this aim, we propose a novel method that leverages on Hidden Markov Models and
Gaussian Graphical Models -- Time Adaptive Gaussian Model (TAGM). Our model is
a generalization of state-of-the-art methods for the inference of temporal
graphical models, its formulation leverages on both aspects of these models
providing better results than current methods. In particular,it performs
pattern recognition by clustering data points in time; and, it finds
probabilistic (and possibly causal) relationships among the observed variables.
Compared to current methods for temporal network inference, it reduces the
basic assumptions while still showing good inference performances.
