Enhancing Winters exponential smoothing: a novel approach with back-casting, Grey Wolf Optimization, and error tracking

Winters Exponential Smoothing (WES) is a widely used method for forecasting time series data, particularly for handling seasonality in both additive and multiplicative models. This study aims to enhance the forecasting performance of the WES method by introducing three key modifications: back-casting for accurate initialization of WES components, the Grey Wolf Optimization (GWO) algorithm for automated parameter tuning, and a sequential error tracking signal (SETS) for adaptive bias correction. Beyond preliminary validations on German temperature data and the Time Series Data Library (TSDL), this research presents an extensive robustness analysis using 40 diverse series from the M4 Forecasting Competition across multiple temporal frequencies (quarterly, monthly, weekly, and hourly). To ensure methodological rigor and mitigate sampling bias, a rolling-origin evaluation protocol and a systematic GWO stability analysis are employed. Furthermore, the model’s real-time adaptability is demonstrated through a one-step-ahead forecasting framework. Experimental results and ablation studies show that the proposed method achieves a superior global mean rank (1.475–1.625), significantly outperforming Auto-ARIMA, ETS, and Seasonal Naive models. Computational complexity and GWO convergence analyses further confirm that the proposed framework is significantly faster than automated ARIMA models while providing robust, high-precision forecasts suitable for large-scale and high-frequency applications.