  While the vast majority of the literature on models for temporal networks
focuses on binary graphs, often one can associate a weight to each link. In
such cases the data are better described by a weighted, or valued, network. An
important well known fact is that real world weighted networks are typically
sparse. We propose a novel time varying parameter model for sparse and weighted
temporal networks as a combination of the fitness model, appropriately
extended, and 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. The result is a flexible approach
where the probability of a link to exist is independent from its expected
weight. This represents a crucial difference with alternative specifications
proposed in the recent literature, with relevant implications for the
flexibility of the model.
  Our approach also accommodates for the dependence of the network dynamics 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.
