Over the last few years modeling of temporal evolution of network data has become a relevant problem for different applications. In this work, we develop novel statistical methods for modeling time series of directed binary networks. The main interests are identifying events associated with structural changes over time and perform short-term link prediction of the network in future periods.

First, we introduce a Bayesian hidden Markov model that uses a stochastic blockmodel to describe the community structure of the network during each period. This model allow us to monitor structural changes in the network and also perform accurate short-term predictions of future links. As an alternative for link prediction, we propose two multinomial logistic regression models using different lasso type penalties including an extension of the autologistic model for network data. In this setting, we are able to provide fast computational algorithms for estimation and prediction using optimization and full Bayesian inference. The performance of the models is illustrated using both simulated and real data from a financial trading network in the NYMEX natural gas futures market.