  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.
