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

In the grey prediction, the GM(1, 1) model is an important type, but it sometimes shows big prediction errors. To improve the prediction precision of GM(1, 1) model, the paper makes improvements from the following three aspects: (1) to improve the data's adaptability to the model, the paper transforms the accumulated generating sequence of original time sequence; (2) to make the model meet the variation characteristics of data, the paper extends the grey action of traditional GM(1, 1) model; (3) to avoid big average simulation or prediction relative error of model, the paper considers the minimum of the maximum of the two errors as the optimization objective function. The new extended grey model is called the GM(1, 1, exp x sin, exp x cos) model. The paper uses an improved particle swarm optimization (PSO) algorithm for the parameter optimization of GM(1, 1, exp x sin, exp x cos) model and thus improves the model's convergence rate and precision. According to the model and method proposed, the paper builds a GM(1, 1, exp x sin, exp x cos) model for China's GDP per capita. Results show that the model has high precision.