Comparative Analysis of SARIMA, Prophet, and a Diagnostic Decomposition-Correction Hybrid for Long-Horizon Lottery Sales Forecasting.

Accurate forecasting of lottery sales is crucial for strategic planning in volatile consumer markets driven by trend shifts, multi-scale seasonality, and calendar effects. This study proposes a Diagnostic Decomposition-Correction Hybrid (DDC-Hybrid) framework integrating Prophet and SARIMA through a residual diagnostics and correction pipeline. Specifically, Prophet is employed to model long-term trend changes and interpretable holiday impacts, while SARIMA is subsequently used to correct the residual series, capturing short-range temporal dependence that remains statistically significant after decomposition. From an information-theoretic perspective, the framework can be viewed as a two-stage uncertainty reduction process, where decomposition extracts low-frequency informative components and residual correction harvests remaining predictive information. Using monthly lottery sales in China (2008-2025), we conduct a comprehensive evaluation of SARIMA, Prophet, and the proposed hybrid approach. The DDC-Hybrid demonstrates improved predictive accuracy, yielding the lowest error rates. Beyond predictive accuracy, we further examine varying holiday effects through statistical testing. We also find that lottery sales contain a pronounced quadrennial (48-month) seasonal cycle associated with mega-sport events, which improves long-horizon stability. The results suggest that the proposed diagnostic hybrid modeling approach enhances forecasting accuracy and provides practical insights for lottery sales management.