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A novel time-varying grey Fourier model for variable amplitude seasonal fluctuation sequences

Xiaomei Liu (School of Mathematics, Physics and Statistics, Shanghai Polytechnic University, Shanghai, China)
Bin Ma (School of Computer and Information Engineering, Institute for Artificial Intelligence, Shanghai Polytechnic University, Shanghai, China)
Meina Gao (School of Mathematics, Physics and Statistics, Shanghai Polytechnic University, Shanghai, China)
Lin Chen (School of Computer and Information Engineering, Institute for Artificial Intelligence, Shanghai Polytechnic University, Shanghai, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 27 March 2024

Issue publication date: 27 June 2024

51

Abstract

Purpose

A time-varying grey Fourier model (TVGFM(1,1,N)) is proposed for the simulation of variable amplitude seasonal fluctuation time series, as the performance of traditional grey models can't catch the time-varying trend well.

Design/methodology/approach

The proposed model couples Fourier series and linear time-varying terms as the grey action, to describe the characteristics of variable amplitude and seasonality. The truncated Fourier order N is preselected from the alternative order set by Nyquist-Shannon sampling theorem and the principle of simplicity, then the optimal Fourier order is determined by hold-out method to improve the robustness of the proposed model. Initial value correction and the multiple transformation are also studied to improve the precision.

Findings

The new model has a broader applicability range as a result of the new grey action, attaining higher fitting and forecasting accuracy. The numerical experiment of a generated monthly time series indicates the proposed model can accurately fit the variable amplitude seasonal sequence, in which the mean absolute percentage error (MAPE) is only 0.01%, and the complex simulations based on Monte-Carlo method testify the validity of the proposed model. The results of monthly electricity consumption in China's primary industry, demonstrate the proposed model catches the time-varying trend and has good performances, where MAPEF and MAPET are below 5%. Moreover, the proposed TVGFM(1,1,N) model is superior to the benchmark models, grey polynomial model (GMP(1,1,N)), grey Fourier model (GFM(1,1,N)), seasonal grey model (SGM(1,1)), seasonal ARIMA model seasonal autoregressive integrated moving average model (SARIMA) and support vector regression (SVR).

Originality/value

The parameter estimates and forecasting of the new proposed TVGFM are studied, and the good fitting and forecasting accuracy of time-varying amplitude seasonal fluctuation series are testified by numerical simulations and a case study.

Keywords

Acknowledgements

The authors are grateful to the editors and the anonymous reviewers for their helpful comments and suggestions.

Citation

Liu, X., Ma, B., Gao, M. and Chen, L. (2024), "A novel time-varying grey Fourier model for variable amplitude seasonal fluctuation sequences", Grey Systems: Theory and Application, Vol. 14 No. 3, pp. 473-490. https://doi.org/10.1108/GS-10-2023-0101

Publisher

:

Emerald Publishing Limited

Copyright © 2024, Emerald Publishing Limited

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