GM(1, 1) model with seasonal dummy variables and its application

To solve the problem that the GM(1, 1) model is difficult to predict seasonal time series accurately, in this paper, seasonal dummy variables are introduced in the GM(1, 1) model as a grey action quantity, and an improved grey model with seasonal dummy variables (GMSD(1, 1)) is proposed. Furthermore, five models including the GMSD(1, 1, x(1)) model, the GMSD(1, 1, x(0)) model, the GMSD(1, 1, b) model, the GMSD(1, 1, exp) model and the GMSD(1, 1, C) model based on GMSD(1, 1) are derived. A group of grey models based on seasonal dummy variables is constructed finally. At the same time, the particle swarm optimization algorithm is used to optimize the analytical expressions in the GMSD(1, 1) model and the GMSD(1, 1, exp) model. Finally, using the quarterly data of hydropower generation in China as an example, the validity and superiority of the GMSD(1, 1) model with seasonal dummy variables and the five derived models derived in this paper are verified. The results show that, compared with the traditional GM(1, 1) model, the GMSD(1, 1) model with seasonal dummy variables and its derived models can more accurately describe the seasonal fluctuations and periodic changes of the system characteristic sequence. © 2020, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.