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Abstract We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models. The models are called reduced auto-regressive (RAR) models. The procedure of the proposed method is composed of three steps: (i) each time series is treated as a basic node of a network, (ii) multivariate RAR models are built and the constituent information in the models is summarized, and (iii) nodes are connected with a directed link based on that summary information. The proposed method is demonstrated for numerical data generated by known systems, and applied to several actual time series of special interest. Although the proposed method can identify connectivity, there are three points to keep in mind: (1) the proposed method cannot always identify nonlinear relationships among components, (2) as constructing RAR models is NP-hard, the network constructed by the proposed method might be near-optimal network when we cannot perform an exhaustive search, and (3) it is difficult to construct appropriate networks when the observational noise is large. Highlights • A method to construct directed networks from multivariate time series is described. • The method is based on an information theoretic reduction of linear auto-regressive models. • The method enables to reveal hidden relationships among multivariate time series data. • The method is generic and can be applied to any kind of multivariate time series data in principle. • The method is applied to two real time series to verify its effectiveness. [ABSTRACT FROM AUTHOR]