Hierarchical Bayesian autoregressive smooth transition time series models
TL;DR
Hierarchical Bayesian smooth transition autoregressive models provide accurate forecasts by accommodating nonlinear regime-switching dynamics while delivering robust uncertainty quantification, which makes them well suited for infectious disease surveillance and public health decision-making in resource-limited, high-uncertainty settings.
Abstract
Public health policy and disease surveillance systems require accurate forecasting of infectious disease dynamics to support timely interventions and resource allocation. However, classical linear time-series models often fail to capture abrupt regime shifts, nonlinear transmission patterns, and heterogeneous reporting commonly observed in surveillance data. This study investigates the practical advantages of hierarchical Bayesian smooth transition autoregressive (BH-STAR) models, including logistic (LSTAR) and exponential (ESTAR) specifications. Performance is evaluated through extensive simulation studies under controlled nonlinear data-generating mechanisms, followed by an empirical application to COVID-19 surveillance data from 53 African countries collected between March 2020 and December 2022. Simulation studies revealed a key directional asymmetry in model misspecification: fitting a logistic transition function to data generated under exponential dynamics resulted in moderate, stable parameter bias, whereas fitting an exponential transition function to logistic dynamics induced severe, compounding bias. Despite this parameter confounding under model misspecification, predictive accuracy remained stable across both data-generating processes. In the empirical application, the BH-STAR models consistently outperformed linear alternatives in out-of-sample forecasting. The hierarchical logistic STAR (HLSTAR) model achieved the highest overall predictive accuracy, reducing validation errors to an MAE of 0.58 and a MdAPE of 12.8%, corresponding to country-level forecast error reductions of 30–50% and overall error reductions exceeding 50% relative to the standard autoregressive benchmark. Hierarchical Bayesian smooth transition autoregressive models provide accurate forecasts by accommodating nonlinear regime-switching dynamics while delivering robust uncertainty quantification. These features make them well suited for infectious disease surveillance and public health decision-making in resource-limited, high-uncertainty settings.