An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption

Dewang Li; Meilan Qiu; Shuiping Yang; Chao Wang; Zhongliang Luo; Dewang Li; Meilan Qiu; Shuiping Yang; Chao Wang; Zhongliang Luo

doi:10.3934/math.20231349

AIMS Mathematics

2023, Volume 8, Issue 11: 26425-26443. doi: 10.3934/math.20231349

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An optimal fractional-order accumulative Grey Markov model with variable parameters and its application in total energy consumption

1.
School of Mathematics and Statistics, Huizhou University, Huizhou 516007, China
2.
Faculty of Computational Mathematics and Cybernetics, Shenzhen MSU-BIT University, Shenzhen 518055, China
3.
School of Electronic and Information Engineering, Huizhou University, Huizhou 516007, China

Received: 30 June 2023 Revised: 10 August 2023 Accepted: 13 August 2023 Published: 15 September 2023
MSC : 62M05, 62M10, 62P05, 62P20,

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.
- FOGMKM (1, 1),
- variable parameters,
- fractional grey models,
- energy consumption,
- parameter estimation and prediction,
- stochastic Markov process
Citation: 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[J]. AIMS Mathematics, 2023, 8(11): 26425-26443. doi: 10.3934/math.20231349

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Abstract

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.

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