New Methods for Network Count Time Series

The original generalized network autoregressive models are poor for modelling count data as they are based on the additive and constant noise assumptions, which is usually inappropriate for count data. We introduce two new models (GNARI and NGNAR) for count network time series by adapting and extending existing count-valued time series models. We present results on the statistical and asymptotic properties of our new models and their estimates obtained by conditional least squares and maximum likelihood. We conduct two simulation studies that verify successful parameter estimation for both models and conduct a further study that shows, for negative network parameters, that our NGNAR model outperforms existing models and our other GNARI model in terms of predictive performance. We model a network time series constructed from COVID-positive counts for counties in New York State during 2020-22 and show that our new models perform considerably better than existing methods for this problem.

💡 Research Summary

The paper addresses a critical gap in the modeling of network‑based count time series. Existing generalized network autoregressive (GNAR) models assume additive Gaussian‑type noise with constant variance, which is unsuitable for integer‑valued data, especially when counts are low. To overcome this limitation, the authors introduce two novel models: the Generalized Network Autoregressive Integer‑valued (GNARI) model and the Nonlinear Generalized Network Autoregressive (NGNAR) model.

GNARI adapts the thinning operation from integer‑valued autoregressive (INAR) processes to a network context. For each node i at time t, the observation is expressed as a sum of thinned past values of the node itself and thinned, weighted contributions from r‑stage neighbours, plus a Poisson innovation. The thinning parameters α and β lie in