Score Driven Generalized Fitness Model for Sparse and Weighted Temporal Networks

TL;DR

This paper introduces a novel score-driven, generalized fitness model for sparse, weighted temporal networks, enabling flexible link and weight dynamics with external variable dependence, demonstrated through interbank market data.

Contribution

It develops a new time-varying parameter model combining fitness and score-driven frameworks for weighted, sparse networks, allowing independent link existence and weight modeling.

Findings

Effective link forecasting in interbank networks

Model captures external variable influences over time

Flexible handling of sparsity and weights

Abstract

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.