This study presents an innovative approach to determining the coefficients of a high-order quasilinear autoregressive model using the Generalized Least Deviations Method (GLDM). The model aims to capture the dynamics of observed state variables over time, employing a set of given functions to relate past observations to current values. The errors in the observations are considered unknown. The core innovation lies in addressing the Cauchy problem within the GLDM framework, which enhances the robustness and precision of parameter estimation for non-linear datasets. GLDM is achieved by incorporating a loss function based on the arctangent function, improving resilience against outliers and non-standard error distributions. Comprehensive computational experiments and statistical validation determine optimal model orders for various datasets, including small NDVI (Normalized Difference Vegetation Index) time series, extensive temperature time series, and large wind speed datasets. The second-order model is most effective for small NDVI datasets, while the fifth-order model excels for large temperature datasets. For wind speed data, despite its large size, the second-order GLDM model demonstrates superior performance due to its ability to balance model complexity with the need for capturing essential dynamics without overfitting. Furthermore, a comparative analysis of GLDM-based models with classical forecasting models demonstrates the superior adaptability and accuracy of GLDM models across different dataset characteristics. This highlights their robustness against outliers and data anomalies. The study underscores the versatility and efficacy of high-order GLDM models as powerful tools in predictive modeling, offering significant improvements over traditional methods.
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Abotaleb, M. O (2025). Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm. Computational Methods for Differential Equations, 13(3), 940-967. doi: 10.22034/cmde.2024.62441.2751
MLA
Abotaleb, M. O. "Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm", Computational Methods for Differential Equations, 13, 3, 2025, 940-967. doi: 10.22034/cmde.2024.62441.2751
HARVARD
Abotaleb, M. O (2025). 'Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm', Computational Methods for Differential Equations, 13(3), pp. 940-967. doi: 10.22034/cmde.2024.62441.2751
CHICAGO
M. O Abotaleb, "Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm," Computational Methods for Differential Equations, 13 3 (2025): 940-967, doi: 10.22034/cmde.2024.62441.2751
VANCOUVER
Abotaleb, M. O Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm. Computational Methods for Differential Equations, 2025; 13(3): 940-967. doi: 10.22034/cmde.2024.62441.2751
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