2024/08/17 by Iryna Bodnarchuk, Bodnarchuk, Iryna, Yuliya Mishura +3
Economics, Econometrics and Finance · Engineering · #60G25 #Complex Systems and Time Series Analysis #Control Systems and Identification #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 60G22. Secondary 60G15 #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2408.09188
openalex publication_date 2024/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.