A novel multivariate grey model for forecasting periodic oscillation time series

Abstract

To solve the problem that the grey multivariate prediction model cannot well simulate systems with periodic oscillations, a novel multivariate grey model called the GM(1,N|sin) power model is proposed. The power exponential term and dynamic sinusoidal function are developed to represent the nonlinear relationship and periodic oscillations of the independent and dependent variables in the proposed model, respectively. First, the discrete time response formula for generating the simulated values at each time point is given. Second, the nonlinear programming model based on the particle swarm optimization algorithm is established to solve the power exponential and periodic coefficients. In addition, to enhance the generalization ability of the parameters, an improved nonlinear programming model considering the accuracy of the validation set is constructed. Finally, in the case studies, the quarterly electricity consumption of Jiangsu Province and PM2.5 concentrations in Nanjing are adopted to test the effectiveness of this model, and the results are obtained respectively through the GM(1,N|sin) power model and alternative models. The results indicate that the accuracy of GM(1,N|sin) power model in the time series with periodic oscillations outperforms the other six models in this paper.