AbstractThis work proposes novel network analysis techniques for multivariate time series. We define the network of a multivariate time series as a graph where vertices denote the components of the process and edges denote non-zero long run partial correlations. We then introduce a two step lasso procedure, called nets, to estimate high-dimensional sparse Long Run Partial Correlation networks. This approach is based on a var approximation of the process and allows to decompose the long run linkages into the contribution of the dynamic and contemporaneous dependence relations of the system. The large sample properties of the estimator are analysed and we establish conditions for consistent selection and estimation of the non-zero long run partial correlations. The methodology is illustrated with an application to a panel of U.S. bluechips.