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

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KARAKULLUKÇU E.

Scientific Reports, cilt.16, sa.1, 2026 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 1
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1038/s41598-026-48175-1
  • Dergi Adı: Scientific Reports
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, Chemical Abstracts Core, EMBASE, MEDLINE, Directory of Open Access Journals, Zoological Record, Academic Search Ultimate (EBSCO), Natural Science Collection (ProQuest), Biological Science Database (ProQuest), Biomedical Reference Collection: Corporate Edition (EBSCO), Health Research Premium Collection (ProQuest)
  • Anahtar Kelimeler: Back-casting, Forecasting, Grey wolf optimization, Winters exponential smoothing
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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.