Dynamic Clustering of Multivariate Time Series: Modeling Time‐Varying Memberships

ABSTRACT We propose an automatic method for clustering multivariate time‐series data based on mixtures of Dynamic Linear Models. Unlike traditional time‐series clustering methods that yield static membership parameters, our approach allows each time series to dynamically change cluster memberships over time. Thus, each time series has a dynamic posterior probability of belonging to each cluster. The proposed mixture model is flexible, assuming a Dirichlet evolution for the mixture weights that enables smooth membership transitions over time. This approach accounts for correlations between weights, thereby avoiding abrupt membership changes caused by outlying observations in the series. Posterior estimates of model parameters and membership probabilities are obtained via Gibbs sampling. Furthermore, we introduce an efficient alternative method based on stochastic expectation maximization and gradient descent to obtain point estimates. We illustrate the proposed method using a tri‐variate panel dataset combining Gapminder and World Bank indicators—life expectancy, GDP per capita, and crude birth rate—for 78 European and African countries from 1960 to 2007. The selected regions provide strong socioeconomic and demographic contrasts, allowing the model to effectively capture temporal and structural changes in cluster membership.