Modelling Nonlinearity and Volatility in Castor Prices: A Comparative Study of ARIMA, ARCH, GARCH and Neural Network Models in Patan Market, Gujarat, India

Abstract

Castor (Ricinus communis L.) is a commercially important non-edible oilseed crop in North Gujarat, and price volatility in its principal markets remains a major source of income risk for growers and traders. This study fitted and compared linear, volatility-based and machine-learning models for the weekly castor price series from the Patan market over the period from January 2004 to December 2024 (1,092 weekly observations constructed as period-average aggregates of daily Agmarknet quotations). The Augmented Dickey-Fuller test confirmed that the series was non-stationary in levels but stationary after first differencing; the Brock-Dechert-Scheinkman test established significant nonlinearity; and the ARCH-LM test confirmed the presence of volatility clustering. Accordingly, an ARIMA(3,1,5) model, an AR(1)-ARCH(3) model, an ARMA(0,1)-GARCH(1,2) model and a feed-forward artificial neural network (14-32-1 architecture) were fitted, and their in-sample and out-of-sample performance was evaluated using RMSE, MSE, MAE and MAPE. Among the econometric models, ARIMA(3,1,5) provided the best level-based fit (RMSE = 663.38; MAPE = 9.79%), whereas ARMA-GARCH outperformed AR-ARCH in modelling conditional variance. The ANN model recorded the lowest error for every metric evaluated (RMSE = 115.31; MAPE = 1.37%), consistent with the nonlinear dependence detected by the BDS test. However, because the ANN was fitted to price levels using engineered lagged and rolling features, whereas the ARCH-family models were fitted to returns, the comparison was not fully equivalent and the performance gap should be interpreted with this caveat. The findings underline the value of combining diagnostic testing with a multi-model framework when characterising agricultural commodity price behaviour.