Comparative statistical modeling of aggregated monthly rainfall in India using ARIMA and seasonal ARIMA models

Introduction Monthly precipitation forecasting supports water-resource planning, agriculture, reservoir operation, and hydrological decision-making. This study compares established statistical time-series models for an aggregated monthly precipitation series representing 36 Indian States and Union Territories, with emphasis on differencing choice, information-criterion comparability, and out-of-sample forecasting performance. Methods Daily NASA POWER PRECTOTCORR data were aggregated to 40 monthly observations from January 2023 to April 2026. An unweighted mean across the 36 State/UT series formed the modeling series. The analysis included data-quality screening, correlation and deseasonalized-anomaly assessment, ADF and KPSS stationarity tests, ACF/PACF diagnostics, and evaluation of AR, MA, ARIMA, and parsimonious SARIMA models. Information criteria were compared only within models with comparable differencing structures and effective sample sizes. Forecast performance was assessed using leakage-free expanding-window rolling-origin validation with 10 one-step-ahead forecasts, using MAE, RMSE, and MASE against a seasonal-naive benchmark. Results The level series showed mixed ADF/KPSS evidence, whereas seasonal differencing alone supported d = 0 and D = 1. SARIMA(0, 0, 0)(0, 1, 0) 12 had the lowest AICc within the seasonal candidate group and was selected at all 10 rolling origins. Its MAE, RMSE, and MASE were 0.6294, 0.7897, and 0.7419, respectively, identical to the seasonal-naive benchmark. The May 2026 forecast was 6.4636 mm/day, with 80 and 95% prediction intervals of 5.1096–7.8177 and 4.3928–8.5344 mm/day, respectively. Discussion The findings show the importance of reassessing differencing, restricting information-criterion comparisons to comparable models, and embedding selection within genuine out-of-sample validation. For this short 40-month aggregated series, the parsimonious seasonal model reduced to the same one-step-ahead structure as the seasonal-naive benchmark, while greater model complexity did not improve forecasting performance.