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The Proof of the Structure Stability of the Polynomial Curve Fitting Model When the Time Variable t Takes Equidistant Values

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  • Zhao Zhang

Abstract

The polynomial curve fitting models are among the most common trend extrapolation prediction models. The time-independent variable t=t1,t2,⋯,tnT can take on various values during model construction, and it is a theoretical question whether different value selections will affect the model’s structure. This study proves that when the time-independent variable t is sampled equidistantly, the least-squares error (SSE) of the established polynomial curve fitting model remains constant, the model validation F-statistic is equal, and the polynomial degree of the model is consistent. The demonstration that equidistant sampling of the time-independent variable maintains structural stability in the model will provide theoretical support for the modeling and application of this model.

Suggested Citation

  • Zhao Zhang, 2026. "The Proof of the Structure Stability of the Polynomial Curve Fitting Model When the Time Variable t Takes Equidistant Values," Journal of Mathematics, Hindawi, vol. 2026, pages 1-7, January.
    • Handle: RePEc:hin:jjmath:2798812
    DOI: 10.1155/jom/2798812
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