Statistical case study analysis of the quantity of water resources in Azerbaijan: Absheron Peninsula

This study develops long-term water supply and demand forecasting models for the Absheron Peninsula of Azerbaijan, a semi-arid region with 4.0 million inhabitants entirely dependent on external water sources. Daily production and consumption data from 2016–2024 are analysed using three complementary specifications: ARMA(2,1) on the level series as a conservative parametric baseline, ARIMA(2,1,1) as a comparison model for assessing the effect of first differencing, and Prophet with automatic trend and seasonality decomposition. A seasonal-naive baseline ( (Formula presented) (Formula presented) ) serves as a non-parametric reference, and forecasts are validated through rolling-origin cross-validation across five hold-out years (2020–2024). Strong annual seasonality is present, with 30%–35% amplitude variation between summer peaks and winter troughs. On the 2024 hold-out, Prophet attains the strongest near-term accuracy (RMSE 0.75 m³ s⁻¹), followed by the seasonal-naive baseline (1.07 m³ s⁻¹); ARMA(2,1) on level (2.30 m³ s⁻¹) outperforms ARIMA(2,1,1) (3.20 m³ s⁻¹) among the ARIMA-family models and is therefore used as the conservative parametric baseline. Long-term projections to 2050 diverge sharply: ARMA(2,1) yields a stable annual surplus of approximately 4.9 Mm³ yr⁻¹ (≈0.87% of supply), ARIMA(2,1,1) approximately 2.8 Mm³ yr⁻¹, and Prophet an expanding surplus reaching 14.8 Mm³ yr⁻¹ by 2050. When the documented 35%–37% transmission and distribution losses are incorporated as a stress-test scenario, all three models project structural deficits of approximately 173–283 Mm³ yr⁻¹ by 2050. The findings underscore the need for multivariate forecasting frameworks, integrated hydrological modelling, and adaptive management strategies for long-term water security.