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Study of the grey Verhulst model based on the weighted least square method

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  • Tang, Liwei
  • Lu, Yayun

Abstract

Analysis is conducted on the sources of several fitting errors of the grey Verhulst model, including approximation construction of the background value, inconsistency among the parameters of the difference and differential forms, the objective function setting of parameter estimation, and so on. However, constructing the precise background value of this model is complicated. A new parameter estimation method based on weighted least squares is proposed by transforming the model and using the approximate transformation of the objective function. Moreover, weights are determined by the converted form of target functions. In addition, the properties of the model under the new parameter form are studied. The proposed model avoids the process of precise background value construction as well as conversion from differential to difference equations. Empirical analysis shows that the method is effective.

Suggested Citation

  • Tang, Liwei & Lu, Yayun, 2020. "Study of the grey Verhulst model based on the weighted least square method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320163
    DOI: 10.1016/j.physa.2019.123615
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    References listed on IDEAS

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    1. Mohammad Hashem-Nazari & Akbar Esfahanipour & S.M.T. Fatemi Ghomi, 2017. "Non-equidistant “Basic Form”-focused Grey Verhulst Models (NBFGVMs) for ill-structured socio-economic forecasting problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 18(4), pages 676-694, July.
    2. Wu, Wenqing & Ma, Xin & Zeng, Bo & Wang, Yong & Cai, Wei, 2019. "Forecasting short-term renewable energy consumption of China using a novel fractional nonlinear grey Bernoulli model," Renewable Energy, Elsevier, vol. 140(C), pages 70-87.
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    Cited by:

    1. Phi-Hung Nguyen & Jung-Fa Tsai & Ihsan Erdem Kayral & Ming-Hua Lin, 2021. "Unemployment Rates Forecasting with Grey-Based Models in the Post-COVID-19 Period: A Case Study from Vietnam," Sustainability, MDPI, vol. 13(14), pages 1-27, July.
    2. Zhou, Chenyu & Shen, Yun & Wu, Haixin & Wang, Jianhong, 2022. "Using fractional discrete Verhulst model to forecast Fujian's electricity consumption in China," Energy, Elsevier, vol. 255(C).

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