Modeling and Forecasting Monthly Rainfall Quantities Using the SARIMA Model: An Applied Study at the Central Park Station in New York

Abstract

This study aims to model and forecast the temporal and seasonal behaviour of monthly rainfall amounts using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model. The study drew on 552 monthly rainfall observations from the New York City Central Park station in New York City, covering the period January 1980 to December 2025, based on NOAA/NCEI data. The analysis revealed statistically significant differences between months, with a continued need to represent the seasonal structure in the model. After examining stationarity, autocorrelation and partial autocorrelation functions, and estimating a set of candidate models, the model was selected as the final model based on information criteria, residual diagnostics and out-of-sample forecasting performance. The data were split into a training sample covering the period 1980–2022 and a test sample covering the period 2025–2023. In the test sample, the model achieved an MAE of 48.52 mm and an RMSE of 66.2 mm, whilst the MASE calculated for the seasonal perspective was 0.749 and the Ljung–Box test showed no significant autocorrelation in the residuals at lags 12, 24 and 36. The model was also used to produce monthly forecasts for the period 1/2027–12/2027.