  The integration of social media characteristics into an econometric framework
requires modeling a high dimensional dynamic network with dimensions of
parameter typically much larger than the number of observations. To cope with
this problem, we introduce SONIC, a new high-dimensional network model that
assumes that (1) only few influencers drive the network dynamics; (2) the
community structure of the network is characterized by homogeneity of response
to specific influencers, implying their underlying similarity. An estimation
procedure is proposed based on a greedy algorithm and LASSO regularization.
Through theoretical study and simulations, we show that the matrix parameter
can be estimated even when sample size is smaller than the size of the network.
Using a novel dataset retrieved from one of leading social media platforms -
StockTwits and quantifying their opinions via natural language processing, we
model the opinions network dynamics among a select group of users and further
detect the latent communities. With a sparsity regularization, we can identify
important nodes in the network.
