  The problem of estimating high-dimensional network models arises naturally in
the analysis of many physical, biological and socio-economic systems. Examples
include stock price fluctuations in financial markets and gene regulatory
networks representing effects of regulators (transcription factors) on
regulated genes in genetics. We aim to learn the structure of the network over
time employing the framework of Granger causal models under the assumptions of
sparsity of its edges and inherent grouping structure among its nodes. We
introduce a thresholded variant of the Group Lasso estimator for discovering
Granger causal interactions among the nodes of the network. Asymptotic results
on the consistency of the new estimation procedure are developed. The
performance of the proposed methodology is assessed through an extensive set of
simulation studies and comparisons with existing techniques.
