IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v138y2020ics0960077920303155.html
   My bibliography  Save this article

Fractional Hausdorff grey model and its properties

Author

Listed:
  • Chen, Yan
  • Lifeng, Wu
  • Lianyi, Liu
  • Kai, Zhang

Abstract

The grey model with the fractional Hausdorff derivative is put forward to enhance the forecasting accuracy of traditional grey model. The proposed model will not be effect by the initial value x(0)(1). The relationship between the error and the order (r) is proved. We also make a comparison among the proposed model with the traditional fractional grey model and the traditional grey model. The comparison results show that the proposed model can improve the traditional grey model.

Suggested Citation

  • Chen, Yan & Lifeng, Wu & Lianyi, Liu & Kai, Zhang, 2020. "Fractional Hausdorff grey model and its properties," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303155
    DOI: 10.1016/j.chaos.2020.109915
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920303155
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109915?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zeng, Bo & Li, Chuan, 2016. "Forecasting the natural gas demand in China using a self-adapting intelligent grey model," Energy, Elsevier, vol. 112(C), pages 810-825.
    2. Liu, Xiaomei & Xie, Naiming, 2019. "A nonlinear grey forecasting model with double shape parameters and its application," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 203-212.
    3. Gatabazi, P. & Mba, J.C. & Pindza, E. & Labuschagne, C., 2019. "Grey Lotka–Volterra models with application to cryptocurrencies adoption," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 47-57.
    4. Yang, Yang & Xue, Dingyü, 2016. "Continuous fractional-order grey model and electricity prediction research based on the observation error feedback," Energy, Elsevier, vol. 115(P1), pages 722-733.
    5. Wu, Wenqing & Ma, Xin & Zeng, Bo & Wang, Yong & Cai, Wei, 2018. "Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption," Energy, Elsevier, vol. 165(PB), pages 223-234.
    6. Wu, Lifeng & Liu, Sifeng & Fang, Zhigeng & Xu, Haiyan, 2015. "Properties of the GM(1,1) with fractional order accumulation," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 287-293.
    7. Gatabazi, P. & Mba, J.C. & Pindza, E., 2019. "Modeling cryptocurrencies transaction counts using variable-order Fractional Grey Lotka-Volterra dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 283-290.
    8. Carmona-Benítez, Rafael Bernardo & Nieto, María Rosa, 2020. "SARIMA damp trend grey forecasting model for airline industry," Journal of Air Transport Management, Elsevier, vol. 82(C).
    9. Zhu, Xiaoyue & Dang, Yaoguo & Ding, Song, 2020. "Using a self-adaptive grey fractional weighted model to forecast Jiangsu’s electricity consumption in China," Energy, Elsevier, vol. 190(C).
    10. Ene, Seval & Öztürk, Nursel, 2017. "Grey modelling based forecasting system for return flow of end-of-life vehicles," Technological Forecasting and Social Change, Elsevier, vol. 115(C), pages 155-166.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wang, Yong & Yang, Zhongsen & Wang, Li & Ma, Xin & Wu, Wenqing & Ye, Lingling & Zhou, Ying & Luo, Yongxian, 2022. "Forecasting China's energy production and consumption based on a novel structural adaptive Caputo fractional grey prediction model," Energy, Elsevier, vol. 259(C).
    2. Xu, Jie & Wu, Wen-Ze & Liu, Chong & Xie, Wanli & Zhang, Tao, 2024. "An extensive conformable fractional grey model and its application," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Wang, Yong & Sun, Lang & Yang, Rui & He, Wenao & Tang, Yanbing & Zhang, Zejia & Wang, Yunhui & Sapnken, Flavian Emmanuel, 2023. "A novel structure adaptive fractional derivative grey model and its application in energy consumption prediction," Energy, Elsevier, vol. 282(C).
    4. Li, Shaohong & Wu, Na, 2021. "A new grey prediction model and its application in landslide displacement prediction," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    5. Wu, Wen-Ze & Zeng, Liang & Liu, Chong & Xie, Wanli & Goh, Mark, 2022. "A time power-based grey model with conformable fractional derivative and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. Luo, Xilin & Duan, Huiming & Xu, Kai, 2021. "A novel grey model based on traditional Richards model and its application in COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    7. Zeng, Bo & He, Chengxiang & Mao, Cuiwei & Wu, You, 2023. "Forecasting China's hydropower generation capacity using a novel grey combination optimization model," Energy, Elsevier, vol. 262(PA).
    8. Liu, Chong & Wu, Wen-Ze & Xie, Wanli & Zhang, Jun, 2020. "Application of a novel fractional grey prediction model with time power term to predict the electricity consumption of India and China," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    9. Zhang, Yunxin & Guo, Huan & Sun, Ming & Liu, Sifeng & Forrest, Jeffrey, 2023. "A novel grey Lotka–Volterra model driven by the mechanism of competition and cooperation for energy consumption forecasting," Energy, Elsevier, vol. 264(C).
    10. Yuan, Hong & Ma, Xin & Ma, Minda & Ma, Juan, 2024. "Hybrid framework combining grey system model with Gaussian process and STL for CO2 emissions forecasting in developed countries," Applied Energy, Elsevier, vol. 360(C).
    11. Ding, Song & Hu, Jiaqi & Lin, Qianqian, 2023. "Accurate forecasts and comparative analysis of Chinese CO2 emissions using a superior time-delay grey model," Energy Economics, Elsevier, vol. 126(C).
    12. Tong, Mingyu & Dong, Jingrong & Luo, Xilin & Yin, Dejun & Duan, Huiming, 2022. "Coal consumption forecasting using an optimized grey model: The case of the world's top three coal consumers," Energy, Elsevier, vol. 242(C).
    13. Li, Xuemei & Wu, Xinran & Zhao, Yufeng, 2023. "Research and application of multi-variable grey optimization model with interactive effects in marine emerging industries prediction," Technological Forecasting and Social Change, Elsevier, vol. 187(C).
    14. Qin, Fuli & Tong, Mingyu & Huang, Ying & Zhang, Yubo, 2024. "Modeling, prediction and analysis of natural gas consumption in China using a novel dynamic nonlinear multivariable grey delay model," Energy, Elsevier, vol. 305(C).
    15. Wang, Yong & Yang, Zhongsen & Ye, Lingling & Wang, Li & Zhou, Ying & Luo, Yongxian, 2023. "A novel self-adaptive fractional grey Euler model with dynamic accumulation order and its application in energy production prediction of China," Energy, Elsevier, vol. 265(C).
    16. He, Jing & Mao, Shuhua & Kang, Yuxiao, 2023. "Augmented fractional accumulation grey model and its application: Class ratio and restore error perspectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 220-247.
    17. Shubei Wang & Xiaoling Yuan & Zhongguo Jin, 2024. "Prediction of Energy-Related Carbon Emissions in East China Using a Spatial Reverse-Accumulation Discrete Grey Model," Sustainability, MDPI, vol. 16(21), pages 1-22, October.
    18. Yang, Zhongsen & Wang, Yong & Zhou, Ying & Wang, Li & Ye, Lingling & Luo, Yongxian, 2023. "Forecasting China's electricity generation using a novel structural adaptive discrete grey Bernoulli model," Energy, Elsevier, vol. 278(C).
    19. Yang, Yang & Wang, Xiuqin, 2022. "A novel modified conformable fractional grey time-delay model for power generation prediction," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    20. Wang, Siwei & Xiao, Xinping & Ding, Qi, 2024. "A novel fractional system grey prediction model with dynamic delay effect for evaluating the state of health of lithium battery," Energy, Elsevier, vol. 290(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiong, Xin & Hu, Xi & Guo, Huan, 2021. "A hybrid optimized grey seasonal variation index model improved by whale optimization algorithm for forecasting the residential electricity consumption," Energy, Elsevier, vol. 234(C).
    2. Ma, Xin & Mei, Xie & Wu, Wenqing & Wu, Xinxing & Zeng, Bo, 2019. "A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China," Energy, Elsevier, vol. 178(C), pages 487-507.
    3. Ding, Song & Tao, Zui & Zhang, Huahan & Li, Yao, 2022. "Forecasting nuclear energy consumption in China and America: An optimized structure-adaptative grey model," Energy, Elsevier, vol. 239(PA).
    4. Wang, Yong & Chi, Pei & Nie, Rui & Ma, Xin & Wu, Wenqing & Guo, Binghong, 2022. "Self-adaptive discrete grey model based on a novel fractional order reverse accumulation sequence and its application in forecasting clean energy power generation in China," Energy, Elsevier, vol. 253(C).
    5. Wang, Zheng-Xin & Li, Dan-Dan & Zheng, Hong-Hao, 2020. "Model comparison of GM(1,1) and DGM(1,1) based on Monte-Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    6. Jules Clément Mba & Sutene Mwambetania Mwambi & Edson Pindza, 2022. "A Monte Carlo Approach to Bitcoin Price Prediction with Fractional Ornstein–Uhlenbeck Lévy Process," Forecasting, MDPI, vol. 4(2), pages 1-11, March.
    7. Wu, Wenqing & Ma, Xin & Zeng, Bo & Wang, Yong & Cai, Wei, 2018. "Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption," Energy, Elsevier, vol. 165(PB), pages 223-234.
    8. Xie, Xuemei & Liu, Xiaojie & Blanco, Cristina, 2023. "Evaluating and forecasting the niche fitness of regional innovation ecosystems: A comparative evaluation of different optimized grey models," Technological Forecasting and Social Change, Elsevier, vol. 191(C).
    9. Wen-Ze Wu & Tao Zhang & Chengli Zheng, 2019. "A Novel Optimized Nonlinear Grey Bernoulli Model for Forecasting China’s GDP," Complexity, Hindawi, vol. 2019, pages 1-10, October.
    10. Wang, Yong & He, Xinbo & Zhou, Ying & Luo, Yongxian & Tang, Yanbing & Narayanan, Govindasami, 2024. "A novel structure adaptive grey seasonal model with data reorganization and its application in solar photovoltaic power generation prediction," Energy, Elsevier, vol. 302(C).
    11. Zhang, Kai & Yin, Kedong & Yang, Wendong, 2022. "Predicting bioenergy power generation structure using a newly developed grey compositional data model: A case study in China," Renewable Energy, Elsevier, vol. 198(C), pages 695-711.
    12. He, Jing & Mao, Shuhua & Kang, Yuxiao, 2023. "Augmented fractional accumulation grey model and its application: Class ratio and restore error perspectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 220-247.
    13. Gazi Murat Duman & Elif Kongar, 2023. "ESG Modeling and Prediction Uncertainty of Electronic Waste," Sustainability, MDPI, vol. 15(14), pages 1-20, July.
    14. Nokhaiz Tariq Khan & Javed Aslam & Ateeq Abdul Rauf & Yun Bae Kim, 2022. "The Case of South Korean Airlines-Within-Airlines Model: Helping Full-Service Carriers Challenge Low-Cost Carriers," Sustainability, MDPI, vol. 14(6), pages 1-19, March.
    15. Huiping Wang & Yi Wang, 2022. "Estimating per Capita Primary Energy Consumption Using a Novel Fractional Gray Bernoulli Model," Sustainability, MDPI, vol. 14(4), pages 1-22, February.
    16. Xie, Wanli & Liu, Caixia & Wu, Wen-Ze & Li, Weidong & Liu, Chong, 2020. "Continuous grey model with conformable fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Yi-Chung Hu, 2021. "Forecasting tourism demand using fractional grey prediction models with Fourier series," Annals of Operations Research, Springer, vol. 300(2), pages 467-491, May.
    18. Siyu Zhang & Liusan Wu & Ming Cheng & Dongqing Zhang, 2022. "Prediction of Whole Social Electricity Consumption in Jiangsu Province Based on Metabolic FGM (1, 1) Model," Mathematics, MDPI, vol. 10(11), pages 1-14, May.
    19. Heng Chen & Cheng Peng & Shuang Guo & Zhi Yang & Wei Lu, 2024. "A decision-support framework for industrial green transformation: empirical analysis of the northeast industrial district in China," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 73(4), pages 1917-1958, December.
    20. Ding, Song & Li, Ruojin & Wu, Shu & Zhou, Weijie, 2021. "Application of a novel structure-adaptative grey model with adjustable time power item for nuclear energy consumption forecasting," Applied Energy, Elsevier, vol. 298(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303155. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.