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### 基于卡尔曼滤波的MGM-多维~AR($p$) 模型的构建及其应用

1. 1. 南京信息工程大学管理工程学院, 南京 210044; 2. 南京信息工程大学江苏省统 计科学研究基地,南京 210044; 3. 南京信息工程大学数学与统计学院, 南京 210044
• 出版日期:2018-04-25 发布日期:2021-06-29

XIONG Pingping , TAN Chengwei , YAN Shuli , YAO Tianxiang. Construction and Application of MGM-Multidimensional AR ($p$) Model Based on Kalman Filter[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 1131-1149.

### Construction and Application of MGM-Multidimensional AR ($p$) Model Based on Kalman Filter

XIONG Pingping1,2 , TAN Chengwei2,3 , YAN Shuli1 , YAO Tianxiang1

1. 1.  School of Management Science and Engineering, Nanjing University of Information Science and Technology, Nanjing210044; 2. Jiangsu Statistical Science Research Base, Nanjing University of Information Science and Technology, Nanjing 210044;3. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044
• Online:2018-04-25 Published:2021-06-29

In this paper, a new hybrid model is proposed to improve the prediction accuracy of multivariate grey model (MGM($1, m$)) when it is used to simulate oscillation data. Firstly, Kalman filter is used to eliminate the noise error in the measurement of observation data. Secondly, according to MGM($1, m$) model, the overall development trend of oscillation data can be well reflected, and the residual error between the simulated value and the real data is close to stable distribution. Therefore, the Multidimensional Stationary Sequence Autoregressive (AR($p$)) model is introduced to analyze the residuals, and the variation rules of the residuals are obtained. Finally, the simulated predicted values of MGM($1, m$) model and the residual values calculated by multidimensional AR($p$) model are integrated to obtain the final results of the MGM-multidimensional AR($p$) model. The new combination model and other three models are applied to an example analysis, and the accuracy and feasibility of the new model are verified by comparative analysis. The results show that the new hybrid model can effectively improve the simulation and prediction accuracy of MGM($1, m$) for oscillation data, and broaden the application range of the model.}
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