Joint estimation of multiple network Granger causal models

Joint regularized modeling framework is presented for the estimation of multiple Granger causal networks. High-dimensional network Granger models focus on learning the corresponding causal effects amongst a large set of distinct time series. They are operationalized through the formalism of Vector Autoregressive Models (VAR). The latter represent a popular class of time series models that has been widely used in applied econometrics and finance. In particular, the setting of the same set of variables being measured on different entities over time is considered (e.g. same set of economic indicators for multiple US states). Moreover, the covariance structure of the error term is assumed to exhibit low rank structure which can be recovered by a factor model. The framework allows to account for both sparsity and potential similarities between the related networks by introducing appropriate structural penalties on the transition matrices of the corresponding VAR models. An alternating directions method of multipliers (ADMM) algorithm is developed for solving the underlying joint estimation optimization problem. The performance of the joint estimation method is evaluated on synthetic data and illustrated on an application involving economic indicators for multiple US states11Code and data are available as online supplement..