The multiple-subject vector autoregression (multi-VAR) model captures heterogeneous temporal dependence across subjects through commonly shared and subject-unique paths (entries) of individual (subject-specific) sparse VAR transition matrices. Available joint penalized regression approaches suffer from statistical inefficiency, whereby the convergence rates of the individual estimators are determined by a subject with the largest sparsity level. An enhanced multi-VAR estimation approach is proposed based on a communication-efficient data integration framework and a suitable identifiability condition in meta-analysis. It is shown that component-wise different convergence rates can be achieved. A hypothesis testing framework is also developed to assess the significance of common paths, as well as the homogeneity of subject-specific paths. Furthermore, a multiple hypothesis test to control the false discovery rate is suggested within a subregion of interest among the entire paths. A simulation study and a real data application compare the performance of the considered methods to other approaches.

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