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Multivariate time series forecasting is of great importance to many scientific disciplines and industrial sectors. The evolution of a multivariate time series depends on the dynamics of its variables and the connectivity network of causal interrelationships among them. Most of the existing time series models do not account for the causal effects among the system's variables and even if they do they rely just on determining the between-variables causality network. Knowing the structure of such a complex network and even more specifically knowing the exact lagged variables that contribute to the underlying process is crucial for the task of multivariate time series forecasting. The latter is a rather unexplored source of information to leverage. In this direction, here a novel neural network-based architecture is proposed, termed LAgged VAriable Representation NETwork (LAVARNET), which intrinsically estimates the importance of lagged variables and combines high dimensional latent representations of them to predict future values of time series. Our model is compared with other baseline and state of the art neural network architectures on one simulated data set and four real data sets from meteorology, music, solar activity, and finance areas. The proposed architecture outperforms the competitive architectures in most of the experiments.