An improved grey multivariable model for predicting industrial energy consumption in China

• An improved grey model with convolution integral GMC(1, n) is proposed.
• A nonlinear optimization model is developed to find the optimal parameters.
• The improved grey multivariable model exhibits a higher accuracy than GMC(1, n), SARMA and GM(1, 1).

A grey forecasting model based on convolution integral (GMC(1, n)) is an accurate grey multivariable model, which is derived from the GM(1, n) model by adding a control parameter u. n interpolation coefficients, as unknown parameters, are input into the background values of the n variables so as to improve the adaptability of GMC(1, n) on real data. In addition, a nonlinear optimization model is constructed to obtain the optimal parameters that can minimize the modelling error. The modelling and forecasting results as applied to China's industrial energy consumption show that the optimized grey multivariable model exhibits a higher accuracy than GMC(1, n), SARMA and GM(1, 1). The method proposed for the optimization of the background value can significantly promote the modelling and forecasting precision of GMC(1, n).