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Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.g. the number of causal features allowed in the prediction. To authors extent none of the existent methods endows the user with full control over the different aspects of the sparsity of the solution. In this article, we propose a versatile sparsity-controlled VAR model which enables a proper visualization of potential causalities while allows the user to control different dimensions of the sparsity if she holds some preferences regarding the sparsity of the outcome. The model coefficients are found as the solution to an optimization problem, solvable by standard numerical optimization routines. The tests performed on both simulated and real-life time series show that our approach may outperform a greedy algorithm and different Lasso approaches in terms of prediction errors and sparsity. [ABSTRACT FROM AUTHOR]