An interactive grey multivariable model based on the dynamic accumulative driving effect and its application

A novel systematic multivariable grey model called the interactive grey multivariable forecasting model based on the dynamic accumulative driving effect (IDCGM(1, N)) is developed to predict the trends of an interactive system. More specifically, a utility function to describe the dynamic relationships between system variables is designed and calculated using the impulse response function of the vector autoregressive regression model (VAR). Accounting for the accumulative impacts of historical variables, the accumulative utility term is used to describe the accumulative driving effects between variables. Considering the complex nonlinear relationships between system variables and time, a time power term is also introduced into the model framework. To improve the model's prediction performance, the particle swarm optimization algorithm (PSO) is used to optimize the nonlinear parameters. To demonstrate the effectiveness of the IDCGM(1, N) model in practice, we assess its performance by fitting seven benchmark models with data from 2000 to 2015 and using these models to produce forecasts for 2016–2019. Results show that the IDCGM(1, N) model achieves an optimal fit and prediction performance compared to other benchmark models, which also describes the inherent interactive relationship of the system composed of the technological innovation investment, energy intensity and carbon emission intensity.