  We develop a variational Bayesian (VB) approach for estimating large-scale
dynamic network models in the network autoregression framework. The VB approach
allows for the automatic identification of the dynamic structure of such a
model and obtains a direct approximation of the posterior density. Compared to
Markov Chain Monte Carlo (MCMC) based sampling approaches, the VB approach
achieves enhanced computational efficiency without sacrificing estimation
accuracy. In the simulation study conducted here, the proposed VB approach
detects various types of proper active structures for dynamic network models.
Compared to the alternative approach, the proposed method achieves similar or
better accuracy, and its computational time is halved. In a real data analysis
scenario of day-ahead natural gas flow prediction in the German gas
transmission network with 51 nodes between October 2013 and September 2015, the
VB approach delivers promising forecasting accuracy along with clearly detected
structures in terms of dynamic dependence.
