glmSTARMA -- An R-Package for fitting autoregressive spatio-temporal models following generalized linear models

2026-07-09

AI Summary

This study addresses the absence of a unified framework for simultaneously modeling temporal lag dependencies, covariate effects, and varying dispersion in fixed-location spatiotemporal count data. Building upon generalized linear models (GLMs), the authors propose an autoregressive spatiotemporal double GLM framework that jointly models both the conditional mean and the dispersion parameter—a first in the context of spatiotemporal count sequences. The mean structure integrates past observations, lagged expectations, and covariates, while the dispersion parameter can flexibly depend on spatiotemporal covariates, accommodating overdispersion, underdispersion, and spatiotemporal GARCH effects. A companion R package provides full functionality for inference, simulation, and forecasting, and the model’s flexibility and practical utility are demonstrated across diverse real-world spatiotemporal datasets, including both count and continuous outcomes.

Abstract

The R package glmSTARMA implements autoregressive models for spatio-temporal data at fixed locations, with time-invariant spatial dependency structure. We rely on generalized linear models methodology and unify several approaches for the analysis of spatial count time series. Such models allow the (conditional) mean of the response to depend on past observations, lagged (conditional) expectations, and covariates. The response can be a continuous or a discrete random variable. Additionally, the package develops inference for double generalized linear models, allowing the dispersion parameter(s) of the marginal distributions to be modeled similarly to the mean process. This is a new capability which introduces, for example, spatio-temporal volatility models, such as space-time GARCH processes, and count time series models with spatio-temporal overdispersion and underdispersion. We provide functions for model estimation, simulation, inference, and prediction. Its use is illustrated by data examples.

Problem

• spatio-temporal data
• autoregressive models
• generalized linear models
• overdispersion
• underdispersion

Innovation

• spatio-temporal modeling
• generalized linear models
• autoregressive models
• double GLM
• overdispersion