Generative Topographic Mapping (GTM) is a latent variable model that, in its original version, was conceived to provide clustering and visualization of multivariate, realvalued, i.i.d. data. It was also extended to deal with noni-i.i.d. data such as multivariate time series in a variant called GTM Through Time (GTM-TT), defined as a constrained Hidden Markov Model (HMM). In this paper, we provide the theoretical foundations of the reformulation of GTM-TT within the Variational Bayesian framework and provide an illustrative example of its application. This approach handles the presence of noise in the time series, helping to avert the problem of data overfitting.