Score-driven generalized fitness model for sparse and weighted temporal networks

Temporal network data have recently received increasing attention due to the rich information content and valuable insight that appropriate modeling of links' dynamics can unveil. While most of the literature on temporal network models focuses on binary graphs, each link of a real networks is often associated with a weight, a positive number describing the intensity of the relation between the nodes. Here we propose a novel dynamical model for sparse and weighted temporal networks as a combination of an extension of the fitness model and of the score-driven framework. We consider a zero-augmented generalized linear model to handle the weights and an observation-driven approach to describe time-varying parameters. We propose a flexible approach where the existence probability of a link is independent of its expected weight. This fact represents a crucial difference with alternative specifications proposed in the recent literature, with relevant implications both for the model's flexibility and for the forecasting capability. Our approach also accommodates the network dynamics' dependence on external variables. We present a link forecasting analysis to data describing the overnight exposures in the Euro interbank market and investigate whether the influence of EONIA rates on the interbank network dynamics has changed over time during the sovereign debt crisis.