Accurate crop yield prediction has become increasingly critical for global food security in the face of climate change and population growth. Traditional prediction methods are constrained by their dependence on costly equipment and multisource data collection, while data silos and the complexity of agricultural data characterized by long prediction cycles and extensive temporal spans present significant obstacles to effective forecasting. Our key innovations address these challenges through an integrated solution. First, we propose Fed-ARIMA-OPARBFN, a novel lightweight model that combines horizontal federated learning with historical yield data analysis, effectively breaking down data silos while reducing deployment costs. Most significantly, we introduce a hybrid time series modeling mechanism that integrates ARIMA analysis with an optimized OPARBFN neural network, enhancing the capture of complex temporal dependencies across extended prediction horizons. Validation using multiregional crop data from Nepal demonstrates that Fed-ARIMA-OPARBFN achieves a coefficient of determination (R2) 6% to 29% higher than centralized learning models while enabling cross-regional data collaboration. Compared with existing multisource approaches, our model attains comparable accuracy with enhanced generalization using only historical yield data, offering developing countries a cost-effective solution for reliable agricultural decision support.