基于复化Simpson公式改进的灰色神经网络组合模型对国民总收入的预测

The Grey Neural Network Combination Model Based on Complex Simpson Formula is Used to Predict the Gross National Income of China

摘要: 针对我国国民总收入数据具有非线性、随机性等特点，本文建立复化Simpson公式改进的灰色神经网络组合预测模型来对我国国民总收入进行预测研究。首先，建立了GM(1,1)模型和基于复化Simpson积分公式改进背景值的GM(1,1)模型。其次，建立了BP神经网络预测模型。进一步，将复化Simpson公式改进的GM(1,1)模型和BP神经网络预测模型进行最优线性加权组合，运用最小二乘法思想，误差平方和最小为目标函数，结合遗传算法求解目标函数，得到各模型的加权系数，以提高预测精度。最后，对比分析GM(1,1)模型、复化Simpson公式改建的GM(1,1)模型、BP神经网络模型和复化Simpson公式改进的灰色神经网络模型对国民总收入预测的结果。从预测结果看出，复化Simpson公式改进的灰色神经网络模型对国民总收入的预测明显优于其他预测模型。

Abstract: Aiming at the non-linearity and randomness of China's gross national income data, this paper establishes a grey neural network combined forecasting model which is improved by using the complex Simpson formula to predict China's gross national income. Firstly, the GM(1,1) model and the GM(1,1) model based on the complex Simpson integral formula to improve the background value are established. Secondly, a BP neural network prediction model is established. Furthermore, the GM(1,1) model and the BP neural network prediction model improved by the complex Simpson formula are optimally linearly weighted, and the objective function is solved by using the genetic algorithm to obtain the objective function with the smallest squared error sum. Weighting factors are to improve prediction accuracy. Finally, the GM(1,1) model, the GM(1,1) model of the modified Simpson formula, the BP neural network model and the improved gray neural network model of the modified Simpson formula are used to compare the results of the gross national income forecast. From the prediction results, the gray neural network model improved by the complex Simpson formula is significantly better than the GM(1,1) model, the GM(1,1) model of the modified Simpson formula and the BP neural network model.