Cross-Validated Adaptive Grey–ARIMA Hybrid forecasting of annual municipal water consumption under structural change: a case study of Suez City, Egypt

Reliable forecasting of municipal water consumption is essential for infrastructure planning and sustainable resource management. However, annual water-consumption records are often short, non-stationary, and affected by structural changes, limiting the effectiveness of data-intensive machine-learning and conventional statistical models. This study proposes a Cross-Validated Adaptive Grey–ARIMA Hybrid (CVA-GAH) model for forecasting annual municipal water consumption from limited historical data. The proposed framework combines a metabolic GM(1,1) model, fitted using a rolling data window, with an autoregressive integrated moving average model in a parallel weighted architecture. Model order, metabolic window length, and combination weight are selected exclusively through walk-forward cross-validation. An Occam’s-razor validation gate is incorporated to retain the hybrid model only when its additional complexity produces a meaningful out-of-sample improvement. The framework was evaluated using a 28-year annual water-consumption dataset from Suez City, Egypt, covering 1997–2024. Data from 1997–2020 were used for model development, while observations from 2021–2024 were reserved as a strictly blind holdout period containing a post-2020 structural decline. Cross-validation selected an ARIMA(0,2,1) model, a six-year metabolic GM(1,1) window, and respective blending weights of 0.85 and 0.15. During the blind holdout evaluation, CVA-GAH achieved a mean absolute percentage error of 4.14%, a mean absolute error of \(3.88× 10⁶\) , and a root mean squared error of \(4.90× 10⁶\) . These results improved upon standalone ARIMA and conventional GM(1,1), while reducing error volatility relative to ARIMA. The findings demonstrate that CVA-GAH provides an interpretable and computationally efficient forecasting framework for small-sample municipal water-demand series, although its empirical performance remains characterized by the specific socio-demographic and structural dynamics of the Suez City case study.