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A Flexible Time Power Grey Fourier Model for Nonlinear Seasonal Time Series and Its Applications.

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Title: A Flexible Time Power Grey Fourier Model for Nonlinear Seasonal Time Series and Its Applications.
Authors: Xiaomei Liu1, Jiannan Zhu2, Meina Gao1 mngao@sspu.edu.cn
Source: Journal of Grey System. 2025, Vol. 37 Issue 1, p43-63. 17p.
Subjects: Sampling theorem, Time series analysis, Wind forecasting, Statistical models, Artificial intelligence
Abstract: Grey Fourier model has been successfully applied in seasonal time series forecasting, but its performance in handling nonlinear seasonal time series may still require further improvement. To describe the nonlinear characteristics, a flexible time power grey Fourier model (TPGFM(1,1,N,r)) is proposed by introducing nonlinear time power terms to the grey action of grey Fourier model. The hyperparameters, the truncated Fourier order N and time power r are initially selected by the Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal parameters are determined by the hold-out method. To further improve the prediction accuracy for nonlinear time sequences, combination models based on the proposed grey model, statistical models and artificial intelligence models are designed. The variable weights are assigned by the inverse variance weighting method. Afterward, the results of the designed experiments based on numerical experiment verify the validity of the Fourier order and time power selection, illustrating the superior performances over benchmark models. Finally, the proposed model is applied for monthly PM2.5 forecasting and quarterly wind power generation forecasting, outperforming other benchmark models in prediction, including seasonal grey models, artificial intelligence models and statistical models. Moreover, the combination models, developed based on TPGFM(1,1,N,r) model, have achieved higher prediction accuracy. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Grey System is the property of Research Information Ltd. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Flexible Time Power Grey Fourier Model for Nonlinear Seasonal Time Series and Its Applications.
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  Data: <searchLink fieldCode="AR" term="%22Xiaomei+Liu%22">Xiaomei Liu</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Jiannan+Zhu%22">Jiannan Zhu</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Meina+Gao%22">Meina Gao</searchLink><relatesTo>1</relatesTo><i> mngao@sspu.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Grey+System%22">Journal of Grey System</searchLink>. 2025, Vol. 37 Issue 1, p43-63. 17p.
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  Data: <searchLink fieldCode="DE" term="%22Sampling+theorem%22">Sampling theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Time+series+analysis%22">Time series analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Wind+forecasting%22">Wind forecasting</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+models%22">Statistical models</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+intelligence%22">Artificial intelligence</searchLink>
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  Label: Abstract
  Group: Ab
  Data: Grey Fourier model has been successfully applied in seasonal time series forecasting, but its performance in handling nonlinear seasonal time series may still require further improvement. To describe the nonlinear characteristics, a flexible time power grey Fourier model (TPGFM(1,1,N,r)) is proposed by introducing nonlinear time power terms to the grey action of grey Fourier model. The hyperparameters, the truncated Fourier order N and time power r are initially selected by the Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal parameters are determined by the hold-out method. To further improve the prediction accuracy for nonlinear time sequences, combination models based on the proposed grey model, statistical models and artificial intelligence models are designed. The variable weights are assigned by the inverse variance weighting method. Afterward, the results of the designed experiments based on numerical experiment verify the validity of the Fourier order and time power selection, illustrating the superior performances over benchmark models. Finally, the proposed model is applied for monthly PM2.5 forecasting and quarterly wind power generation forecasting, outperforming other benchmark models in prediction, including seasonal grey models, artificial intelligence models and statistical models. Moreover, the combination models, developed based on TPGFM(1,1,N,r) model, have achieved higher prediction accuracy. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Grey System is the property of Research Information Ltd. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 17
        StartPage: 43
    Subjects:
      – SubjectFull: Sampling theorem
        Type: general
      – SubjectFull: Time series analysis
        Type: general
      – SubjectFull: Wind forecasting
        Type: general
      – SubjectFull: Statistical models
        Type: general
      – SubjectFull: Artificial intelligence
        Type: general
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      – TitleFull: A Flexible Time Power Grey Fourier Model for Nonlinear Seasonal Time Series and Its Applications.
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            NameFull: Xiaomei Liu
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            NameFull: Jiannan Zhu
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            NameFull: Meina Gao
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            – D: 01
              M: 01
              Text: 2025
              Type: published
              Y: 2025
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