Quantifying rainfall-induced climate risk in rainfed agriculture: A volatility-based time series study from semi-arid India

Intra-annual variation in rainfall creates significant challenges for agricultural output, particularly in semi-arid monsoon regions. In this study, we present a volatility-in-mean time series modeling framework to examine how rainfall risk influences rice yield forecasts in Maharashtra, India. We construct four distinct measures to capture intra-seasonal rainfall variability and incorporate them into forecasting models using six decades of monthly rainfall data (1962–2021) for the state. These measures are embedded within ARIMAX and GARCH-ARIMAX specifications to jointly assess the effects of rainfall volatility on the mean and variability of yields. Our results show that volatility-based models – especially exponential GARCH (eGARCH) and gjrGARCH variants using higher-order, first-difference-based measures ($R{V}_3$ and $R{V}_4$) – consistently deliver superior forecast accuracy and greater robustness compared to simpler ARIMAX or iGARCH configurations. Models relying on contemporaneous rainfall volatility outperform those using lagged measures, underscoring the immediate impact of seasonal climate anomalies. Sensitivity analysis with $\pm 10$% perturbations to rainfall risk measures further confirms that GARCH-type models not only improve predictive skill but also enhance stability under plausible input variations, making their inclusion effectively indispensable for climate-sensitive crop forecasting. These findings reinforce the need to embed dynamic meteorological risk indicators in agricultural forecasting frameworks to strengthen early warning systems, support adaptive policy design, and promote resilient, sustainable cropping systems in monsoon-dependent regions.