PNAR Models for Population Dynamics in Complex Networks: A High-Dimensional Approach

This paper analyzes population dynamics in Asturias (Spain) using a network-based time series framework. This setting constitutes a complex system where interactions between settlements shape aggregate population outcomes. We model interdependencies between settlements through a complex network derived from the provision of secondary education services. We compare two approaches: the generalized network autoregressive (GNAR) model and the Poisson network autoregressive (PNAR) model. While GNAR provides a flexible representation of network dependencies, it faces limitations in high-dimensional settings with short time series. PNAR, by contrast, offers a more suitable framework for count data and improves model stability and interpretability. Using empirical estimation and simulation, we show that population dynamics are primarily driven by temporal persistence, but also influenced by network interactions. Moreover, counterfactual simulations based on alternative network structures suggest that more balanced connectivity patterns may enhance local population outcomes. Our results highlight the importance of model choice in network time series and demonstrate that PNAR models provide a robust computational framework for high-dimensional network count data, with potential applications to other complex systems.