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The Method of Optimal Non-Linear Extrapolation of Vector Random Functions on the Basis of Canonical Expansion
Subject area: Science,Engineering and Technology · Area of research: Machine Learning
Abstract
Nonlinear extrapolation of vector random functions plays a pivotal role in numerous scientific and engineering applications, such as signal processing, financial forecasting, machine learning, and turbulence modeling. Conventional linear extrapolation techniques, including Wiener filtering and autoregressive moving average (ARMA) models, often fail to account for the intricate dependencies and higher-order interactions present in non-Gaussian data. While canonical expansions provide an optimal representation of vector random functions through orthogonal basis function decomposition, they remain insufficient for effective nonlinear extrapolation. A more advanced approach is required to capture higher-order dependencies and multi-scale structures inherent in complex real-world datasets. This study explores the limitations of traditional methods and proposes a robust framework for nonlinear extrapolation, addressing the challenges posed by non-Gaussian statistics and multi-scale variability.
References
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How to cite this paper
@article{1707359,
author = {Ayobami Michael Opefeyijimi},
title = {The Method of Optimal Non-Linear Extrapolation of Vector Random Functions on the Basis of Canonical Expansion},
journal = {Iconic Research And Engineering Journals},
year = {2025},
volume = {8},
number = {9},
pages = {76-82},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1707359.pdf},
abstract = {Nonlinear extrapolation of vector random functions plays a pivotal role in numerous scientific and engineering applications, such as signal processing, financial forecasting, machine learning, and turbulence modeling. Conventional linear extrapolation techniques, including Wiener filtering and autoregressive moving average (ARMA) models, often fail to account for the intricate dependencies and higher-order interactions present in non-Gaussian data. While canonical expansions provide an optimal representation of vector random functions through orthogonal basis function decomposition, they remain insufficient for effective nonlinear extrapolation. A more advanced approach is required to capture higher-order dependencies and multi-scale structures inherent in complex real-world datasets. This study explores the limitations of traditional methods and proposes a robust framework for nonlinear extrapolation, addressing the challenges posed by non-Gaussian statistics and multi-scale variability.},
month = {March},
}