Hybrid Time-Series Approaches for Soybean Price Forecasting Using Linear and Non-Linear Models

Abstract

Soybean is an important agricultural commodity, essential for food security, livestock feed, and industrial uses. Therefore, understanding its price fluctuations is critical for informed decision-making. However, soybean prices show significant volatility due to fluctuations in global demand and supply, climate variability, and policy alterations, resulting in uncertainty for farmers, traders, and policymakers. This study aims to examine the time-series dynamics of soybean prices and establish an accurate forecasting framework using a monthly dataset from January 1960 to March 2026 obtained from the World Bank. The study uses various forecasting methodologies, comprising linear models (ARIMA, ETS, and Theta), a nonlinear model (NNAR), and hybrid models that combine linear and nonlinear frameworks, with model performance determined through accuracy metrics including Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). The findings reveal that soybean prices show considerable variability, averaging $292.59 per metric ton, ranging from $88.00 to $737.06, indicating high market volatility. Furthermore, while the ARIMA (1,1,3) model effectively identifies linear trends, the NNAR model shows superior performance among individual models by yielding reduced forecasting errors (RMSE = 162.86; MAPE = 36.22%). The hybrid ARIMA–NNAR model attains superior accuracy, significantly reducing forecast errors (RMSE = 98.03; MAPE = 21.66%). This highlights the benefits of integrating linear and nonlinear methods. The forecast indicates that soybean prices are expected to rise in the short-term, peak in 2027–2028, and then decline gradually toward 2030. However, the expanding prediction intervals show growing uncertainty over time. The findings confirm that hybrid models provide a more robust and reliable framework for forecasting soybean prices. Future studies should integrate exogenous variables such as climatic conditions, trade policies, and exchange rates, and should investigate new methodologies, including deep learning approaches, to improve forecasting precision and policy relevance.