Abstract: Abstract: Treating historical data as equivalent in energy forecasting systems fails to capture structural differences and temporal dynamics, restricting model performance under complex, non-stationary conditions. Against this background, the identification of key points, serving as the critical method of capturing internal structural changes within data sequences, plays a vital role in enhancing the model’s ability to perceive dynamic patterns, improving the stability of energy forecasting systems and optimizing the overall performance. To tackle this issue, the neighborhood similarity function based on the Gaussian kernel function is constructed, which enables differentiated processing of historical data information in energy prediction system, and by incorporating this approach with the recursive weighted least squares method for dynamic updating of model parameters, the recursive grey multivariable prediction model based on neighborhood similarity is proposed. Based on the recursive method, the iteration formulation for parameter estimation of the recursive grey multivariable prediction model based on neighborhood similarity is derived. Furthermore, the parameter optimization framework for the model is established by integrating the particle swarm optimization algorithm. With this as the foundation, the recursive grey multivariable prediction model based on neighborhood similarity proposed in this study is applied to predict the total electricity generation in Jiangsu Province and the total residential natural gas consumption in China. Research results show that: the recursive grey multivariable prediction model based on neighborhood similarity proposed in this study outperforms other classical models in both fitting and forecasting precision. Meanwhile, the ablation experiments are conducted on the proposed recursive grey multivariable prediction model based on neighborhood similarity using data of the primary electricity and other energy consumption in China. By gradually eliminating improvement strategies during the experimental process, the contribution of each component of the recursive grey multivariable prediction model based on neighborhood similarity proposed in this study to the overall performance is evaluated. Finally, the China’s total primary electricity and other energy consumption in 2024-2025 are forecasted with the recursive grey multivariable prediction model based on neighborhood similarity proposed in this paper.

Key words: neighborhood similarity, recursive weighted least squares, grey multivariable prediction model, energy forecasting system