The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Our interest lies in joint, multi-class estimation of several VAR models. Assume we have K VAR models for K distinct but related classes. We jointly estimate these K VAR models to borrow strength across classes and to estimate multiple models that share certain characteristics. Our methodology encourages corresponding effects to be similar across classes, while still allowing for small differences between them. Moreover, we focus on multi-class estimation of high-dimensional VAR models, i.e. models with a large number of parameters relative to the time series length. Therefore, our estimate is sparse: unimportant effects are estimated as exactly zero, which facilitates the interpretation of the results. We consider a multi-store marketing application on cross-category management and a multi-market macro-economic application on commodity price dynamics of the proposed methodology.