A Robust Hybrid Forecasting Framework for the M3 and M4 Competitions: Combining ARIMA and Ata Models with Performance-Based Model Selection

This study proposes a hybrid forecasting framework that integrates the Auto-Regressive Integrated Moving Average (ARIMA) model with multiple variations of the Ata model, using a performance-based model selection strategy to enhance forecasting accuracy on the M3 and M4 competition datasets. For each time series, seven versions of the Ata model are generated by adjusting level and trend parameters, and the version with the lowest in-sample symmetric mean absolute percentage error (sMAPE) is selected. To improve robustness and prevent overfitting, the median-performing Ata model is also included. These selected models’ forecasts are then combined with ARIMA outputs through optimized weighting schemes tailored to the characteristics of each series. Given the varying frequencies (e.g., yearly, quarterly, monthly, weekly, daily, and hourly) and diverse lengths of time series, a grid search algorithm is employed to determine the best hybrid combination for each frequency group. The model is applied in a series-specific manner, allowing it to adapt to different seasonal, trend, and irregular patterns. Extensive empirical results demonstrate that the hybrid model outperforms its individual components and traditional benchmarks across all frequency categories. It ranked first in the M3 competition and achieved second place in the M4 competition based on the official error metric, the sMAPE and Overall Weighted Average (OWA), respectively. The results highlight the framework’s adaptability and scalability for complex, heterogeneous time series environments.