基于正负残差马尔可夫灰色预测模型及应用

Forecasting Model and Application Based on Positive and Negative Residual Markov Grey

当前对于数据预测的精度要求日益增高,这是因为预测数据能够为未来的规划与决策提供更有效的依据。数据的变化规律可以利用灰色系统进行捕捉,但传统的灰色GM(1,1)模型已经不能够有效地预测出精度较高的数据。因而,文章通过引用马尔可夫方法对正负残差进行合理调整,利用马尔可夫能够处理数据的波动性特点,结合以上两种方法从而提出精确度更高的正负残差Markov灰色预测方法。以浙江省2000—2019年铁路客运量作为原始数据序列进行模型的拟合,通过比较GM(1,1)和正负残差Markov灰色GM(1,1)的误差精度,发现改进后的GM(1,1)模型更加适用于未来数据的预测。

At present,the precision requirements for data prediction are growing increasingly.This is because forecasting data can provide more effective basis for future planning and decision-making.The changing law of the data can be captured by the gray system,but the original gray GM(1,1)model can no longer effectively predict the data with higher accuracy.Therefore,this article uses the Markov method to reasonably adjust the positive and negative residuals,take advantage of the volatility characteristics of the data that Markov can handle,and combines the above two methods to propose a more accurate Markov gray prediction method for positive and negative residuals.In this paper,the railway passenger traffic volume from 2000 to 2019 in Zhejiang Province is used as the original data sequence to fit the model.As a result,the improved GM(1,1)model is more suitable for forecasting future data by comparing the error accuracy of GM(1,1)and positive and negative residual Markov gray GM(1,1).