Fractional Gaussian Noise: Projections, Prediction, Norms

We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst in...

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Bibliographic Details
Main Authors: Iryna Bodnarchuk, Yuliya Mishura, Kostiantyn Ralchenko
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Fractal and Fractional
Subjects:
Online Access:https://www.mdpi.com/2504-3110/9/7/428
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Summary:We examine the one-sided and two-sided (bilateral) projections of an element of fractional Gaussian noise onto its neighboring elements. We establish several analytical results and conduct a numerical study to analyze the behavior of the coefficients of these projections as functions of the Hurst index and the number of neighboring elements used for the projection. We derive recurrence relations for the coefficients of the two-sided projection. Additionally, we explore the norms of both types of projections. Certain special cases are investigated in greater detail, both theoretically and numerically.
ISSN:2504-3110