IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v360y2019icp203-212.html
   My bibliography  Save this article

A nonlinear grey forecasting model with double shape parameters and its application

Author

Listed:
  • Liu, Xiaomei
  • Xie, Naiming

Abstract

The solution of Bernoulli differential equation can be described as a generalized Logistic curve function. Weibull cumulative distribution function is also an analytic solution of one variable coefficient differential equation. But, however because of the exact analytical solution problem of the equation, up to now, the developing coefficient of all the grey forecasting models is still defined as a constant. So, the aim of this paper is just to construct a novel grey differential equation model by combining NGBM(1,1) and Weibull cumulative distribution function. The proposed model(WBGM(1,1)) has the advantages of NGBM(1,1) and Weibull cumulative distribution. Where there are double shape parameters, the developing coefficient of the grey forecasting model is extended to be a variant. Property analysis of WBGM(1,1) shows that the fitting accuracy is higher and the applicable confines are wider. Finally, this paper gives an optimization method for the parameters of WBGM(1,1). A classic example and a practical case are studied for confirming the effectiveness of WBGM(1,1). The case study is the prediction for the number of invention patents of integrated circuit(IC) filed in China from 2007 to 2017. Results of the example and case study are compared to other forecasting models, including GM(1,1), NGBM(1,1), Holt exponential smoothing and ARIMA. Results show that WBGM(1,1) is a more general and more efficient model in grey prediction theory.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:360:y:2019:i:c:p:203-212
    DOI: 10.1016/j.amc.2019.05.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319304059
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.05.012?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. Zheng-Xin Wang, 2017. "A Weighted Non-linear Grey Bernoulli Model for Forecasting Non-linear Economic Time Series with Small Data Sets," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 169-186.
    2. Chen, Chun-I, 2008. "Application of the novel nonlinear grey Bernoulli model for forecasting unemployment rate," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 278-287.
    3. Chang, Che-Jung & Li, Der-Chiang & Huang, Yi-Hsiang & Chen, Chien-Chih, 2015. "A novel gray forecasting model based on the box plot for small manufacturing data sets," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 400-408.
    4. Sun, Xu & Sun, Wangshu & Wang, Jianzhou & Zhang, Yixin & Gao, Yining, 2016. "Using a Grey–Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China," Tourism Management, Elsevier, vol. 52(C), pages 369-379.
    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. 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).
    2. Wen-Ze Wu & Chong Liu & Wanli Xie & Mark Goh & Tao Zhang, 2023. "Predictive analysis of the industrial water-waste-energy system using an optimised grey approach: A case study in China," Energy & Environment, , vol. 34(5), pages 1639-1656, August.
    3. Chen, Yan & Lifeng, Wu & Lianyi, Liu & Kai, Zhang, 2020. "Fractional Hausdorff grey model and its properties," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Wenqing Wu & Xin Ma & Bo Zeng & Yuanyuan Zhang & Wanpeng Li, 2021. "Forecasting short-term solar energy generation in Asia Pacific using a nonlinear grey Bernoulli model with time power term," Energy & Environment, , vol. 32(5), pages 759-783, August.
    5. 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.
    6. 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.
    7. 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).

    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. Wang, Zheng-Xin & Jv, Yue-Qi, 2021. "A non-linear systematic grey model for forecasting the industrial economy-energy-environment system," Technological Forecasting and Social Change, Elsevier, vol. 167(C).
    2. 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.
    3. Ling-Ling Pei & Qin Li, 2019. "Forecasting Quarterly Sales Volume of the New Energy Vehicles Industry in China Using a Data Grouping Approach-Based Nonlinear Grey Bernoulli Model," Sustainability, MDPI, vol. 11(5), pages 1-15, February.
    4. Xinyu Han & Rongrong Li, 2019. "Comparison of Forecasting Energy Consumption in East Africa Using the MGM, NMGM, MGM-ARIMA, and NMGM-ARIMA Model," Energies, MDPI, vol. 12(17), pages 1-24, August.
    5. Liu, Jintao & Chen, Liangchao & Xu, Wei & Feng, Mingfei & Han, Yongming & Xia, Tao & Geng, Zhiqiang, 2023. "Novel production prediction model of gasoline production processes for energy saving and economic increasing based on AM-GRU integrating the UMAP algorithm," Energy, Elsevier, vol. 262(PB).
    6. En-Chih Chang, 2018. "Improving Performance for Full-Bridge Inverter of Wind Energy Conversion System Using a Fast and Efficient Control Technique," Energies, MDPI, vol. 11(2), pages 1-16, January.
    7. NGO, Hoang Anh & HOANG, Thai Nam, 2020. "A Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM(1,1) and application in predicting total COVID-19 cases," OSF Preprints 6y95m, Center for Open Science.
    8. Dan Ma & Haibo Bai, 2015. "Groundwater inflow prediction model of karst collapse pillar: a case study for mining-induced groundwater inrush risk," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 76(2), pages 1319-1334, March.
    9. 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.
    10. He, Yan-Lin & Wang, Ping-Jiang & Zhang, Ming-Qing & Zhu, Qun-Xiong & Xu, Yuan, 2018. "A novel and effective nonlinear interpolation virtual sample generation method for enhancing energy prediction and analysis on small data problem: A case study of Ethylene industry," Energy, Elsevier, vol. 147(C), pages 418-427.
    11. Liu, Liwei & Zong, Haijing & Zhao, Erdong & Chen, Chuxiang & Wang, Jianzhou, 2014. "Can China realize its carbon emission reduction goal in 2020: From the perspective of thermal power development," Applied Energy, Elsevier, vol. 124(C), pages 199-212.
    12. Adriana AnaMaria Davidescu & Simona-Andreea Apostu & Liviu Adrian Stoica, 2021. "Socioeconomic Effects of COVID-19 Pandemic: Exploring Uncertainty in the Forecast of the Romanian Unemployment Rate for the Period 2020–2023," Sustainability, MDPI, vol. 13(13), pages 1-22, June.
    13. 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).
    14. 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.
    15. Kuang, Bing & Lu, Xinhai & Zhou, Min & Chen, Danling, 2020. "Provincial cultivated land use efficiency in China: Empirical analysis based on the SBM-DEA model with carbon emissions considered," Technological Forecasting and Social Change, Elsevier, vol. 151(C).
    16. Yi-Chung Hu, 2022. "Demand forecasting of green metal materials using non-equidistant grey prediction with robust nonlinear interval regression analysis," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(8), pages 9809-9831, August.
    17. Wang, Qiang & Song, Xiaoxin, 2019. "Forecasting China's oil consumption: A comparison of novel nonlinear-dynamic grey model (GM), linear GM, nonlinear GM and metabolism GM," Energy, Elsevier, vol. 183(C), pages 160-171.
    18. Ma, Xuejiao & Wang, Yong & Wang, Chen, 2017. "Low-carbon development of China's thermal power industry based on an international comparison: Review, analysis and forecast," Renewable and Sustainable Energy Reviews, Elsevier, vol. 80(C), pages 942-970.
    19. Wei, Sun & Yanfeng, Xu, 2017. "Research on China's energy supply and demand using an improved Grey-Markov chain model based on wavelet transform," Energy, Elsevier, vol. 118(C), pages 969-984.
    20. Yi-Chung Hu & Peng Jiang, 2017. "Forecasting energy demand using neural-network-based grey residual modification models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(5), pages 556-565, May.

    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:360:y:2019:i:c:p:203-212. 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.