Long-memory dynamics and weather-adjusted forecasting of greengram prices: A comparative analysis of ARFIMA, ARIMAX and ARFIMAX models

Abstract

Green gram (Vigna radiata L.), commonly known as mung bean, holds significant importance in Indian agriculture as a protein-rich pulse crop with substantial export potential. Price volatility in green gram markets presents considerable challenges for farmers, traders, and policymakers. This study investigates long-memory dynamics and the impact of weather variables on green gram price forecasting through a comparative analysis of three advanced time-series models: ARFIMA (AutoRegressive Fractionally Integrated Moving Average), ARIMAX (AutoRegressive Integrated Moving Average with eXogenous variables), and ARFIMAX (AutoRegressive Fractionally Integrated Moving Average with eXogenous variables). Monthly price data from Khammam Market, Telangana (April 2022 to May 2025) and corresponding weather variables (minimum temperature, maximum temperature, rainfall, and relative humidity) from NASA POWER were analyzed. Results demonstrate that the ARFIMAX model (AIC: -208.22) outperforms both ARFIMA (AIC: -211.96) and ARIMAX (AIC: -104.76) in forecasting accuracy. The fractional differencing parameter (d = 0.465) indicates significant long-memory characteristics in green gram prices, reflecting persistent price dependencies. Relative humidity emerged as the most influential weather variable (coefficient: -0.0528), followed by maximum temperature (-0.0325). Model diagnostic tests confirm excellent residual properties (Shapiro-Wilk p-value: 0.4725). The six-month forecast (June-November 2025) predicts prices ranging from ₹6,521 to ₹6,588 per quintal with 95% confidence intervals. These findings provide valuable insights for agricultural market participants and contribute to improved decision-making in pulse crop trading and risk management.