Modeling long-term growth and variability of rapeseed and mustard in lucknow district of Uttar Pradesh: A comparative analysis of linear and nonlinear time series models

Rapeseed and mustard are vital oilseed crops in Uttar Pradesh, India, contributing to agricultural livelihoods and food security. This study analyzes long-term trends and variability in area, production, and yield in Lucknow district from 1999–2000 to 2022–23 using linear and nonlinear time series models. Data on area (hectares), production (tonnes), and yield (tonnes/hectare) were modeled with Linear, Power, Mechanistic Growth, Logistic 3-Parameter (3P), and Gompertz 3P models. The Linear model best described area and production, while the Logistic 3P model outperformed for yield, capturing its sigmoidal growth. Challenges include managing high data variability due to weather and policy fluctuations and ensuring convergence of nonlinear models. Results show modest growth in area (+57.8 ha/year) and production (+133.5 t/year), with yield rising (+0.015 t/ha/year). High variability (coefficient of variation: 25.7% for area, 46.2% for production, 31.4% for yield) and instability indices (19.5%–34.3%) suggest external influences like weather or policy changes. Decomposition analysis revealed that yield improvements drove 60.2% of production growth, particularly post-2012 (73.6%). Sensitivity analysis confirmed model robustness, and residual diagnostics validated fit. Forecasts predict stable yields (0.97 t/ha by 2027) and modest increases in area and production. Compared to Uttar Pradesh’s higher yields (1.0–1.2 t/ha), Lucknow’s lag suggests policy needs for hybrid seeds and irrigation. These findings, supported by transparent data access, inform sustainable agricultural planning. This study contributes reliable forecasting tools for regional agricultural planning, a reproducible methodology via transparent data access and insights into the efficacy of Linear versus Nonlinear models for oilseed crops, advancing sustainable agriculture in resource-constrained regions.