Adaptive Forecasting of Epidemiological Time Series with Data-Driven Structural Break Detection: A Comparative Study of Enhanced ARIMA, GAM, and Piecewise Models

Abstract

Accurately forecasting epidemic dynamics is a central challenge in statistical epidemiology, particularly when structural breaks induced by policy interventions or behavioral shifts violate the stationarity assumptions of standard forecasting models. This study introduces a unified framework that augments three widely used model classes—Autoregressive Integrated Moving Average (ARIMA), Generalized Additive Models (GAM), and Piecewise Regression—by embedding an endogenous, data-driven change-point detection mechanism based on volatility shifts. We contrast the performance of conventional baseline models with their adaptive “Change-Point” (CP) counterparts, which explicitly incorporate statistically significant volatility-driven regime changes. Using daily COVID-19 incidence data, we conduct a rigorous comparative evaluation of these approaches. We expand the evaluation metrics to include Symmetric Mean Absolute Percentage Error (SMAPE) and Theil’s U statistic to ensure robustness. Our findings show that systematically accounting for structural breaks consistently enhances predictive accuracy across all model families. A notable bias–variance trade-off emerges: while the flexible Change-Point GAM (CP-GAM) attains the best in-sample fit (Adjusted R² = 0.955), the more parsimonious CP-Piecewise model delivers superior out-of-sample forecasts, achieving the lowest Root Mean Square Error (RMSE) and favorable information criteria. Overall, this work offers a statistically principled methodology for modeling nonstationary epidemiological time series and provides reliable forecasting tools to support evidence-based public health decision-making.