We develop a new class of parsimonious models to perform time-varying clustering and dimensionality reduction in a time-series setting, also accounting for atypical observations. The problem of similarity search in time-series data is addressedby specifying a hidden Markov model. Accordingly, clustering is not only based on similarities in the variable space, but also on similarities occurring in a temporal neighborhood, relaxing the assumption that data points are mutually independent. For the maximum likelihood estimation of the model parameters, we outline an ad-hoc Alternating Expected Conditional Maximization (AECM)algorithm.