Multi-variable grey model based on dynamic background algorithm for forecasting the interval sequence

•The matrix algorithm of a dynamic background value for the interval sequence is proposed.•The multi-variable grey model in matrix form can directly predict the interval sequence.•New model essentially combines two bounds of the interval to predict one of them.•New model well fits the extreme points of electricity consumption in different seasons. The multi-variable grey model based on dynamic background algorithm improves the forecasting performance of the multi-variable grey model on the precise number sequence. In order to make this model suitable for the interval sequence, the matrix form of the multi-variable grey model based on dynamic background algorithm is proposed in the paper. In the modeling process, the interval is treated as a two-dimensional column vector, the parameters of the multi-variable grey model are replaced by matrices, and the dynamic background algorithm for interval sequences is proposed. The analysis results of the matrix algorithm for the dynamic background value and the prediction formula show that the new model is essentially a way to predict one of the two bounds of an interval by combining them, reflecting the integrity and interaction between the lower and upper bounds. The interval predictions of industrial electricity consumption of Zhejiang Province, China national electricity consumption and consumer price index show that the new model can well predict the minimum and maximum values of the interval sequence and has better prediction performance compared with the method of predicting each boundary sequence separately.