Advances in spatial integer-valued time series modeling

This study develops an empirical Bayes (EB) spatial hurdle INGARCH model for weekly dengue fever counts and compares it with a spatial zero-inflated generalized Poisson (ZIGP) INGARCH framework, both of which capture spatio-temporal dependence and excess zeros. The EB-hurdle model introduces a data-adaptive empirical Bayes prior, reduces the number of parameters, and improves parsimony and stability while preserving flexibility for dynamic zero-inflation. In all spatial INGARCH models, the zero mechanism depends on lagged outcomes, so covariate effects enter the intensity equation indirectly. To enhance epidemiological relevance, this study incorporates seasonal components into the log-intensity equations using two approaches: periodic harmonic terms based on Fourier series and meteorological covariates. Model inference is conducted within a Bayesian framework, and performance is evaluated using the Deviance Information Criterion (DIC), Bayes factors, and predictive accuracy metrics, including mean squared error (MSE), mean absolute error (MAE), and mean absolute scaled error (MASE). The results highlight the distinct roles of seasonal and environmental covariates in dengue transmission dynamics. Modeling periodic effects with Fourier terms proves effective, especially when explicit meteorological data are unavailable or incomplete. The empirical Bayes approach enhances parsimony and stability over conventional hurdle INGARCH models.