Purpose Accurate prediction of energy consumption is essential to provide data reference for policy makers in energy-related sectors, while existence of mixed patterns, including linear, nonlinear and time-varying effects, makes its prediction complicated. To effectively capture dynamics in time series, a novel mixed effects-based multivariate gray model is proposed to improve the prediction performance. Design/methodology/approach First, the nonlinear and time-effect terms are introduced into the typical multivariate gray model with convolution integral, which aims to simultaneously capture mixed dynamics in diverse sequences. Second, the gray wolf optimizer (GWO) algorithm is applied to identify the optimal model parameters. Additionally, a Monte-Carlo simulation is conducted to assess the computational efficacy and prediction performance of the novel model combined with GWO. Findings Three real-world cases, namely energy consumption data from three countries, are utilized to evaluate the robustness and reliability of the novel model compared with others. The numerical results show that the novel model enables the identification of the mixed dynamics of energy consumption systems and then enhances the accuracy performance in forecasting energy consumption. Originality/value A novel mixed effects-based multivariate gray model is introduced, which is supported by rigorous mathematical proofs of its properties. Additionally, three case studies compare this model with eight other benchmark models.
Wu et al. (Mon,) studied this question.