Abstract:

To address the nonlinear, non-stationary, and high-noise characteristics of main vegetable price series in Hebei Province, as well as the problem that the kernel extreme learning machine (KELM) relies on empirical parameter settings, which limits its prediction accuracy, this paper constructs a multivariate combined forecasting model integrating the grey wolf optimizer (GWO) and a dual-channel KELM to improve short-term vegetable price prediction accuracy. The weekly wholesale price data of 10 major vegetable varieties (Chinese cabbage, cabbage, tomato, cucumber, potato, green pepper, scallion, garlic, bean, and zucchini) in Hebei Province from January 2021 to December 2024 are collected, with a total sample size of 2,080 records. Eight categories of external features (meteorological, holiday, agricultural material prices, refined oil prices, Weibo public opinion, Baidu index, macro-economic indicators, and food consumption) comprising 28 variables are also collected. Missing values are imputed by mean interpolation, outliers are corrected based on the 3σ principle, and Min-Max normalization is applied to eliminate dimensional effects. First, the Granger causality test is used to verify the predictive causal relationship between external features and vegetable prices, and for the sake of model parsimony and training efficiency, the eight most significant features per variety are retained. Then, a dual-channel parallel KELM model is constructed: Channel 1 takes the price history (4 weeks) and Channel 2 takes the selected external features. The kernel matrices of the two channels are fused by a learnable weight α. The GWO algorithm is introduced to automatically optimize the regularization coefficient C, kernel parameters σ₁ and σ₂, and the fusion weight α, using the root mean square error (RMSE) on the validation set as the fitness function with a population size of 15 and 50 iterations. The proposed model (M3) is compared with a single-channel model using only price history (M1), a single-channel feature-concatenation model (M2), as well as three mainstream models (SVM, LSTM, GRU). The dual-channel GWO-KELM model (M3) achieves an average mean absolute percentage error (MAPE) of 7.52% across the 10 varieties, which is 3.07 percentage points lower than that of M1 (10.59%) and 1.60 percentage points lower than that of M2 (9.12%), and significantly outperforms deep learning methods such as LSTM (9.87%) and GRU (9.56%). The improvement is particularly significant for highly volatile varieties, such as scallion (MAPE reduced from 13.76% to 9.85%). The fusion weight α shows that price-stable varieties (garlic α=0.81, potato α=0.76) rely more on historical inertia, while highly volatile varieties (scallion α=0.48, cucumber α=0.54) depend more on external features, with a negative correlation between α and the coefficient of price variation (r≈−0.73). Contribution analysis of external features indicates that temperature, agricultural material prices, holiday/opinion indicators, and refined oil prices are important leading indicators for vegetable prices. The model also exhibits good generalization on untrained varieties (eggplant, celery, lettuce), with MAPEs of 7.98%, 9.12%, and 12.06%, respectively, and its seasonal error increase is controlled within 1 percentage point. The dual-channel GWO-KELM model constructed in this paper effectively solves the problem of empirical parameter setting of KELM. By integrating Granger causality verification and dual-channel kernel fusion, it achieves adaptive integration of temporal features and heterogeneous external features. The model demonstrates high accuracy, strong generalization ability and good robustness in forecasting main vegetable prices in Hebei Province, and can provide scientific decision support for government regulation, enterprise operations and farmer production.

Key words: Grey Wolf Optimizer, kernel extreme learning machine, Granger causality test, vegetable price prediction, Hebei Province, dual-channel model