An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption
In this paper, we propose an optimal fractional-order accumulative Grey Markov model with variable parameters (FOGMKM (1, 1)) to predict the annual total energy consumption in China and improve the accuracy of energy consumption forecasting. The new model is built upon the traditional Grey model and...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231349?viewType=HTML |
| _version_ | 1797663574656548864 |
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| author | Dewang Li Meilan Qiu Shuiping Yang Chao Wang Zhongliang Luo |
| author_facet | Dewang Li Meilan Qiu Shuiping Yang Chao Wang Zhongliang Luo |
| author_sort | Dewang Li |
| collection | DOAJ |
| description | In this paper, we propose an optimal fractional-order accumulative Grey Markov model with variable parameters (FOGMKM (1, 1)) to predict the annual total energy consumption in China and improve the accuracy of energy consumption forecasting. The new model is built upon the traditional Grey model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The particle swarm optimization algorithm (PSO) is used to determine the number of optimal fractional order and nonlinear parameters. An experiment is conducted to validate the high prediction accuracy of the FOGMKM (1, 1) model, with mean absolute percentage error (MAPE) and root mean square error (RMSE) values of 0.51% and 1886.6, respectively, and corresponding fitting values of 0.92% and 6108.8. These results demonstrate the superior fitting performance of the FOGMKM (1, 1) model when compared to other six competitive models, including GM (1, 1), ARIMA, Linear, FAONGBM (1, 1), FGM (1, 1) and FOGM (1, 1). Our study provides a scientific basis and technical references for further research in the finance as well as energy fields and can serve well for energy market benchmark research. |
| first_indexed | 2024-03-11T19:16:39Z |
| format | Article |
| id | doaj.art-edaaa26ccb2a41338ca259677d39d307 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T19:16:39Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-edaaa26ccb2a41338ca259677d39d3072023-10-09T01:38:13ZengAIMS PressAIMS Mathematics2473-69882023-09-01811264252644310.3934/math.20231349An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumptionDewang Li 0Meilan Qiu 1Shuiping Yang2Chao Wang3Zhongliang Luo41. School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China1. School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China1. School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China2. Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, Shenzhen 518055, ChinaSchool of Electronic and Information Engineering, Huizhou University, Huizhou 516007, ChinaIn this paper, we propose an optimal fractional-order accumulative Grey Markov model with variable parameters (FOGMKM (1, 1)) to predict the annual total energy consumption in China and improve the accuracy of energy consumption forecasting. The new model is built upon the traditional Grey model and utilized matrix perturbation theory to study the natural and response characteristics of a system when the structural parameters change slightly. The particle swarm optimization algorithm (PSO) is used to determine the number of optimal fractional order and nonlinear parameters. An experiment is conducted to validate the high prediction accuracy of the FOGMKM (1, 1) model, with mean absolute percentage error (MAPE) and root mean square error (RMSE) values of 0.51% and 1886.6, respectively, and corresponding fitting values of 0.92% and 6108.8. These results demonstrate the superior fitting performance of the FOGMKM (1, 1) model when compared to other six competitive models, including GM (1, 1), ARIMA, Linear, FAONGBM (1, 1), FGM (1, 1) and FOGM (1, 1). Our study provides a scientific basis and technical references for further research in the finance as well as energy fields and can serve well for energy market benchmark research.https://www.aimspress.com/article/doi/10.3934/math.20231349?viewType=HTMLfogmkm (1， 1)variable parametersfractional grey modelsenergy consumptionparameter estimation and predictionstochastic markov process |
| spellingShingle | Dewang Li Meilan Qiu Shuiping Yang Chao Wang Zhongliang Luo An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption AIMS Mathematics fogmkm (1， 1) variable parameters fractional grey models energy consumption parameter estimation and prediction stochastic markov process |
| title | An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption |
| title_full | An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption |
| title_fullStr | An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption |
| title_full_unstemmed | An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption |
| title_short | An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption |
| title_sort | optimal fractional order accumulative grey markov model with variable parameters and its application in total energy consumption |
| topic | fogmkm (1， 1) variable parameters fractional grey models energy consumption parameter estimation and prediction stochastic markov process |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231349?viewType=HTML |
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