Stochastic Modelling for Tomato Price Forecasting

Abstract

Accurate forecasting of agricultural commodity prices is critical for food security planning, supply-chain management, and policy formulation. Tomato prices exhibit high volatility, seasonal cycles, and intermittent price spikes that challenge classical time series models. Classical linear time series tools such as ARIMA and exponential smoothing tend to miss these features. This study tests whether three continuous time stochastic models can do better which are Geometric Brownian Motion (GBM), the Orntein-Unhenbeck (OU) mean reversion process, and the Jump Diffusion (JD) variant that graft random price jumps onto the OU framework. Weekly tomato price data from the Malaysian market (sourced from FAMA) spanning 207 observations were used, split 80/20 into training and test sets. Each model was run through 100 Monte Carlo paths and the mean path was compared against actual prices. GBM recorded the worst errors (MSE 4.2937, RMSE 2.0721). Among the three stochastic models, OU performed best (MSE 3.7850, RMSE 1.9455), with JD a close second (MSE 3.8454, RMSE 1.9610). A supplementary LSTM baseline, however, outperformed all three stochastic models on raw forecast accuracy (MSE 2.0249, 46% lower than OU, Diebold–Mariano p < 0.0001), indicating that the stochastic models’ advantage lies in interpretability rather than best-in-class point accuracy. A 52-weeks forward forecast with uncertainty bounds was subsequently generated using the OU model. The results point clearly to mean reversion as the key dynamic in tomato pricing, and suggest that stochastic process models can serve as useful interpretable probabilistic tools even where machine learning achieves higher point-forecast accuracy.