Application of a novel grey model GM(1, 1, exp × sin, exp × cos) in China’s GDP per capita prediction

Abstract

In the grey prediction, the GM (1, 1) model is an important type, but it sometimes shows big prediction errors and thus has limitations in applications. To improve the prediction precision of GM (1, 1) model, the paper improves from the following two aspects: (1) to improve the data's adaptability to the model, the paper transforms the accumulated generating sequence of original time sequence to make the transformed sequence meet the laws presented by the model; (2) because the traditional GM (1, 1) model's residual sequence generally shows a sine-cosine fluctuating state with a weak tendency, the paper extends the grey action of traditional GM (1, 1) model. The extended grey model is called the GM (1, 1, exp×sin, exp×cos) model. The paper gives the parameter optimization and time response equation of GM (1, 1, exp×sin, exp×cos) model. The traditional optimization method has its limitations, generally requiring the information such as the gradient value of objective function, and shows a slow convergence rate and poor precision. The paper gives a modern intelligent optimization algorithm, i.e. the particle swarm optimization algorithm (PSO), which has strong robustness and a fast convergence rate and can be realized easily and used flexibly. To improve the algorithm's convergence rate and precision, the paper improves the traditional PSO properly. According to the model and method proposed, the paper builds a GM (1, 1, exp×sin, exp×cos) model for China's GDP per capita. Results show that the model has high precision.