丽江海外旅游人数预测的GM(1,1)模型优化

Optimization of GM(1,1) Model for the Prediction of the Number of Overseas Tourists in Lijiang

分析传统灰色GM(1,1)模型存在的缺陷,从数据处理、初值选取与背景值改进三个角度提出一种GM(1,1)模型的综合优化方法.对原始数据进行线性对数-指数函数变换,以预测值与真实值的误差平方和最小原则重选初值,用累加序列拟合曲线积分重构背景值.综合优化的GM(1,1)模型应用于丽江海外旅游人数预测,与传统GM(1,1)模型对比,平均相对误差从2.43%改进为2.07%,关联度检验效果由"不满意"提高到"满意".

The defects of the traditional grey GM（1,1） model were analyzed, and a comprehensive optimization method of GM（1,1） model was proposed from three aspects： data processing, initial value selection and background value improve- ment. The original data were transformed from linear logarithm to exponential function. Initial value was reselected ac- cording to the principle of minimizing sum of error squares of the predicted values and the real value. Background values was reconstructed with integral of fitting curve of accumulated sequence. The comprehensive optimization GM（1,1） model was applied to forecast the number of overseas tourists in Lijiang. Compared with the traditional GM（1,1） model, the aver- age relative error is improved from 2.43% to 2.07%, and the test effect of correlation degree is improved from unsatisfactory to satisfactory.