IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v252y2015icp287-293.html
   My bibliography  Save this article

Properties of the GM(1,1) with fractional order accumulation

Author

Listed:
  • Wu, Lifeng
  • Liu, Sifeng
  • Fang, Zhigeng
  • Xu, Haiyan

Abstract

For traditional grey model (GM(1,1)), it is proved theoretically that the initial condition is not utilized, and the simulative value is convex and increased or is the decreased and concave when the actual sequence is nonnegative increased. These shortcomings are the results of traditional first order accumulation on grey system model. However, for the GM(1,1) with fractional order accumulation, the initial condition is utilized, and the monotonicity and convexity of simulative value are uncertain when the actual value is nonnegative increased. The results of practical numerical examples demonstrate that the GM(1,1) with fractional order accumulation provides very remarkable predication performance compared with the traditional GM(1,1) model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:287-293
    DOI: 10.1016/j.amc.2014.12.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314016683
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.12.014?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. Li, Der-Chiang & Chang, Che-Jung & Chen, Chien-Chih & Chen, Wen-Chih, 2012. "Forecasting short-term electricity consumption using the adaptive grey-based approach—An Asian case," Omega, Elsevier, vol. 40(6), pages 767-773.
    2. Shun-Xiang Wu & De-Lin Luo & Zhi-Wen Zhou & Jian-Huai Cai & Yeu-Xiang Shi, 2011. "A kind of BP neural network algorithm based on grey interval," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(3), pages 389-396.
    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. Gazi Murat Duman & Elif Kongar, 2023. "ESG Modeling and Prediction Uncertainty of Electronic Waste," Sustainability, MDPI, vol. 15(14), pages 1-20, July.
    2. 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.
    3. İhsan Erdem Kayral & Tuğba Sarı & Nisa Şansel Tandoğan Aktepe, 2023. "Forecasting the Tourist Arrival Volumes and Tourism Income with Combined ANN Architecture in the Post COVID-19 Period: The Case of Turkey," Sustainability, MDPI, vol. 15(22), pages 1-20, November.
    4. 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).
    5. Yi-Chung Hu, 2023. "Tourism combination forecasting using a dynamic weighting strategy with change-point analysis," Current Issues in Tourism, Taylor & Francis Journals, vol. 26(14), pages 2357-2374, July.
    6. 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.
    7. 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.
    8. Ye, Li & Dang, Yaoguo & Fang, Liping & Wang, Junjie, 2023. "A nonlinear interactive grey multivariable model based on dynamic compensation for forecasting the economy-energy-environment system," Applied Energy, Elsevier, vol. 331(C).
    9. 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.
    10. Chen, Yan & Lifeng, Wu & Lianyi, Liu & Kai, Zhang, 2020. "Fractional Hausdorff grey model and its properties," Chaos, Solitons & Fractals, Elsevier, vol. 138(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. Zhang, Chonghui & Bai, Chen & Su, Weihua & Balezentis, Tomas, 2024. "The centralised data envelopment analysis model integrated with cost information and utility theory for power price setting under carbon peak strategy at the firm-level," Energy, Elsevier, vol. 292(C).
    2. Feng, Qianqian & Sun, Xiaolei & Hao, Jun & Li, Jianping, 2021. "Predictability dynamics of multifactor-influenced installed capacity: A perspective of country clustering," Energy, Elsevier, vol. 214(C).
    3. Ye, Li & Yang, Deling & Dang, Yaoguo & Wang, Junjie, 2022. "An enhanced multivariable dynamic time-delay discrete grey forecasting model for predicting China's carbon emissions," Energy, Elsevier, vol. 249(C).
    4. Adedayo Ajayi & Patrick Chi-Kwong Luk & Liyun Lao & Mohammad Farhan Khan, 2023. "Energy Forecasting Model for Ground Movement Operation in Green Airport," Energies, MDPI, vol. 16(13), pages 1-19, June.
    5. Hu, Huanling & Wang, Lin & Lv, Sheng-Xiang, 2020. "Forecasting energy consumption and wind power generation using deep echo state network," Renewable Energy, Elsevier, vol. 154(C), pages 598-613.
    6. Tuncay Özcan, 2017. "Application of Seasonal and Multivariable Grey Prediction Models for Short-Term Load Forecasting," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 5(2), pages 329-338, December.
    7. Wei Zhou & Demei Zhang, 2016. "An Improved Metabolism Grey Model for Predicting Small Samples with a Singular Datum and Its Application to Sulfur Dioxide Emissions in China," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-11, February.
    8. Weiwei Pan & Lirong Jian & Tao Liu, 2019. "Grey system theory trends from 1991 to 2018: a bibliometric analysis and visualization," Scientometrics, Springer;Akadémiai Kiadó, vol. 121(3), pages 1407-1434, December.
    9. Yongtong Shao & Tao Xiong & Minghao Li & Dermot Hayes & Wendong Zhang & Wei Xie, 2021. "China's Missing Pigs: Correcting China's Hog Inventory Data Using a Machine Learning Approach," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(3), pages 1082-1098, May.
    10. Yi-Chung Hu, 2017. "Nonadditive Grey Prediction Using Functional-Link Net for Energy Demand Forecasting," Sustainability, MDPI, vol. 9(7), pages 1-14, July.
    11. Wang, Lin & Hu, Huanling & Ai, Xue-Yi & Liu, Hua, 2018. "Effective electricity energy consumption forecasting using echo state network improved by differential evolution algorithm," Energy, Elsevier, vol. 153(C), pages 801-815.
    12. Yi-Chung Hu, 2017. "Electricity consumption prediction using a neural-network-based grey forecasting approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(10), pages 1259-1264, October.
    13. 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.
    14. Wu, Wen-Ze & Pang, Haodan & Zheng, Chengli & Xie, Wanli & Liu, Chong, 2021. "Predictive analysis of quarterly electricity consumption via a novel seasonal fractional nonhomogeneous discrete grey model: A case of Hubei in China," Energy, Elsevier, vol. 229(C).
    15. OA Carboni & P. Russu, 2014. "Measuring Environmental and Economic Efficiency in Italy: an Application of the Malmquist-DEA and Grey Forecasting Model," Working Paper CRENoS 201401, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    16. Ma, Weimin & Zhu, Xiaoxi & Wang, Miaomiao, 2013. "Forecasting iron ore import and consumption of China using grey model optimized by particle swarm optimization algorithm," Resources Policy, Elsevier, vol. 38(4), pages 613-620.
    17. Zhao, Huiru & Guo, Sen, 2016. "An optimized grey model for annual power load forecasting," Energy, Elsevier, vol. 107(C), pages 272-286.
    18. Yi-Chung Hu, 2017. "Predicting Foreign Tourists for the Tourism Industry Using Soft Computing-Based Grey–Markov Models," Sustainability, MDPI, vol. 9(7), pages 1-12, July.
    19. Atif Maqbool Khan & Magdalena Osińska, 2021. "How to Predict Energy Consumption in BRICS Countries?," Energies, MDPI, vol. 14(10), pages 1-21, May.
    20. Qasem Abu Al-Haija, 2021. "A Stochastic Estimation Framework for Yearly Evolution of Worldwide Electricity Consumption," Forecasting, MDPI, vol. 3(2), pages 1-11, April.

    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:apmaco:v:252:y:2015:i:c:p:287-293. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.