A Methodological Comparison of Forecasting Models Using KZ Decomposition and Walk-Forward Validation

Khawla Al-Saeedi (), Diwei Zhou (), Andrew Fish, Katerina Tsakiri and Antonios Marsellos
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Khawla Al-Saeedi: Department of Statistics Techniques, Institute of Administration/Rusafa, Middle Technical University (MTU), Muaskar Al-Rashid Street, Baghdad 10047, Iraq
Diwei Zhou: Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
Andrew Fish: Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK
Katerina Tsakiri: Department of Information Systems, Analytics and Supply Chain Management, Rider University, Lawrenceville, NJ 08648, USA
Antonios Marsellos: Department of Geology, Environment and Sustainability, Hofstra University, Hempstead, NY 11549, USA

Mathematics, 2025, vol. 13, issue 21, 1-25

Abstract: The accurate forecasting of surface air temperature (T2M) is crucial for climate analysis, agricultural planning, and energy management. This study proposes a novel forecasting framework grounded in structured temporal decomposition. Using the Kolmogorov–Zurbenko (KZ) filter, all predictor variables are decomposed into three physically interpretable components: long-term, seasonal, and short-term variations, forming an expanded multi-scale feature space. A central innovation of this framework lies in training a single unified model on the decomposed feature set to predict the original target variable, thereby enabling the direct learning of scale-specific driver–response relationships. We present the first comprehensive benchmarking of this architecture, demonstrating that it consistently enhances the performance of both regularized linear models (Ridge and Lasso) and tree-based ensemble methods (Random Forest and XGBoost). Under rigorous walk-forward validation, the framework substantially outperforms conventional, non-decomposed approaches—for example, XGBoost improves the coefficient of determination ( R 2 ) from 0.80 to 0.91. Furthermore, temporal decomposition enhances interpretability by enabling Ridge and Lasso models to achieve performance levels comparable to complex ensembles. Despite these promising results, we acknowledge several limitations: the analysis is restricted to a single geographic location and time span, and short-term components remain challenging to predict due to their stochastic nature and the weaker relevance of predictors. Additionally, the framework’s effectiveness may depend on the optimal selection of KZ parameters and the availability of sufficiently long historical datasets for stable walk-forward validation. Future research could extend this approach to multiple geographic regions, longer time series, adaptive KZ tuning, and specialized short-term modeling strategies. Overall, the proposed framework demonstrates that temporal decomposition of predictors offers a powerful inductive bias, establishing a robust and interpretable paradigm for surface air temperature forecasting.

Keywords: time series forecasting; Kolmogorov–Zurbenko filter; multi-scale decomposition; Ridge regression; Lasso regression; Random Forest; XGBoost; environmental data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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