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This article proposes a Bayesian nonparametric method for forecasting,imputation, and clustering in sparsely observed, multivariate time series data.The method is appropriate for jointly modeling hundreds of time series withwidely varying, non-stationary dynamics. Given a collection of $N$ time series,the Bayesian model first partitions them into independent clusters using aChinese restaurant process prior. Within a cluster, all time series are modeledjointly using a novel "temporally-reweighted" extension of the Chineserestaurant process mixture. Markov chain Monte Carlo techniques are used toobtain samples from the posterior distribution, which are then used to formpredictive inferences. We apply the technique to challenging forecasting andimputation tasks using seasonal flu data from the US Center for Disease Controland Prevention, demonstrating superior forecasting accuracy and competitiveimputation accuracy as compared to multiple widely used baselines. We furthershow that the model discovers interpretable clusters in datasets with hundredsof time series, using macroeconomic data from the Gapminder Foundation.

Temporally-Reweighted Chinese Restaurant Process Mixtures for Clustering, Imputing, and Forecasting Multivariate Time Series