Stochastic Time Series Analysis for Palay Production in South Cotabato, Philippines, Using the Seasonal Autoregressive Integrated Moving Average (SARIMA) Model

Abstract

This study used SARIMA time series modeling to describe, model, and forecast quarterly palay production in South Cotabato, Philippines using data from 1987 to 2025 (i.e., 1987–2019 as training period and 2020–2025 as validation period), and then generate forecasts from 2026 to 2030. Specifically, it aimed to explore dynamics of palay production, determine the best SARIMA model specification, assess model forecasting ability, and create forecasts of future production. Results show that palay production shows a rising trend over the long term, together with a very significant seasonal variation with seasonality s = 4. Palay production peaks in Q3 and Q4 and bottoms out in Q2 every year. From among 29 potential model specifications, SARIMA(0,1,1)(1,1,1)[4] proved to be the optimal specification according to various criteria. The analysis of residuals shows that the model is good at capturing not only the seasonal component but also the non-seasonal one with residuals resembling white noise. Accuracy assessment of forecasts showed that the model has acceptable and stable accuracy both in-sample and out-of-sample. Even though the model underestimates production when validated, the errors made by the model in training data and validation data do not vary significantly, implying generalization without overfitting. The predicted level of palay production between 2026 to 2030 will be steady and feature recurring seasonal variations, with no increase or decrease in production over the five-year period considered. The prediction intervals widen as the length of prediction horizon increases, reflecting rising uncertainty about forecasts.