## 1 Introduction
The central tenet of this approach is to refine the current forecast by incorporating the immediate error [19]. Neural networks have robust capabilities for self-learning and adaptation, allowing them to approximate complex nonlinear functions with high accuracy and making them ideal for predicting agricultural prices. The BPNN, GRNN, and ELM are among the neural network models frequently employed in this domain [2; 20]. Nevertheless, there is a dearth of models that focus on residual correction, especially those based on SVR and ELM. The performance of SVR is highly contingent on its penalty factors and kernel function parameters, which significantly affect the model's convergence rate and accuracy [21]. Similarly, the randomly determined input weights and hidden layer biases of ELM can influence its learning efficiency and generalization ability [22; 23]. In contrast to other algorithms, the sparrow search algorithm (SSA) distinguishes itself by its streamlined structure, minimal control parameters, precise solutions, and rapid convergence in optimization tasks [24; 25]. This study utilizes SSA to optimize the penalty factors and kernel function parameters of SVR, as well as to fine-tune the input weights and hidden layer biases of ELM, thereby enhancing the predictive accuracy of both the SVR and ELM models. Traditional ensemble forecasting models assign uniform weight coefficients to the same single model at all time points within a sample interval. However, the accuracy of a single model can vary at different time points, revealing a limitation of the conventional ensemble forecasting approach. To overcome this, the induced ordered weighted averaging (IOWA) operator is introduced, which allocates weights to each individual forecasting model based on their accuracy at each specific time point within the sample interval. To deal with the nonlinear, random, and multi-periodic intricacies that are inherently present in agricultural price time series, the aim of this research is to establish a forecasting approach that makes use of a combined residual correction strategy. At the beginning, the SSA is utilized to optimize the penalty factors and kernel function parameters of the SVR model, along with the input weights and hidden layer biases of the ELM model, with the intention of improving their predictive precision. Then, the IOWA operator is adopted to assign weights to each separate forecasting technique based on the accuracy of their fit at each particular time point within the sample period. This resolves the problem of the same weight coefficients being allotted to the same single forecasting method at every time point within the sample interval. Eventually, the residuals of the GRNN model are predicted by the optimal neural network residual correction method guided by the IOWA operator, resulting in an adjusted final forecast. To validate the effectiveness of the proposed model, it is applied to the dataset of the monthly pork price in Beijing, China, ranging from January 2009 to September 2024, with predictions for pork prices extending from October 2024 to December 2025. The establishment of a highly precise and practical pork price forecasting model will assist in uncovering the pattern of pork price variations. Furthermore, it will offer a significant decision-making foundation for producers and operators, as well as for the government to formulate appropriate regulatory policies and measures. This paper is organized as follows: Section 2 conducts a review of the literature concerning price forecasting models, Section 3 elaborates on the construction of the proposed model, and Section 4 validates the model's validity, makes a comparison with other forecasting models, and discusses the forecasting outcomes. Section 5 concludes the paper through an analysis.