Quarterly Data Forecasting Method Based on Extended Grey GM(2, 1, Σsin) Model and Its Application in China’s Quarterly GDP Forecasting

In the grey prediction, the GM(N, 1) model is an important type. There are relatively more studies on the GM(2, 1) model, but most scholars used the GM(2, 1) model to explore the prediction problem of monotone time sequences and only a few scholars used the GM(2, 1) model to predict non-monotone time sequences, such as the quarterly variation sequence. The paper uses the GM(2, 1) model to predict quarterly variation sequences. To improve the modeling precision, the paper makes improvements in the following three aspects: (1) to improve quarterly data’s adaptability to the model, the paper improves the original time sequence, i.e. introducing a quarterly multiple factor for a data transformation of the original time sequence; (2) to make the model present quarterly data’s variation characteristics, the paper improves the traditional GM(2, 1) model’s structure, i.e. introducing a superposed trigonometric function to extend the model’s grey action; (3) to improve the model’s simulation and prediction precision, the paper improves the parameter optimization method, i.e. considering the minimum of the maximum of average simulation and prediction relative errors as the objective function. The results of this study are as follows: (1) the introduction of seasonal multiplication factor enhances the adaptability of quarterly data to the model; (2) the expanded model can reflect the characteristics of seasonal data changes; (3) examples show that the simulation and prediction accuracies of the expanded model are very high, and the average simulation relative error is only 1.44%, and the average prediction relative error is only 1.43%. The errors are very small; (4) the simulation and prediction accuracies of the extended model are significantly higher than those of the traditional and comparative models.