Дослідження впливу наявності меж при симуляції фрактального броунівського руху на точність оцінки показника Херста

Abstract

This work is devoted to the influence of boundaries on the estimation of the Hurst exponent during Fractional Brownian Motion simulations in the second Anomalous Diffusion (AnDi) challenge. Ten key methods for estimating the Hurst exponent were applied to experiments with varying series lengths and diffusion coefficients for persistent time series with a Hurst exponent above 0.75. The findings reveal that all examined methods, except for the periodogram method, are susceptible to boundary effects even at short series lengths. The periodogram method proved to be robust against boundary effects when working with persistent time series across all tested series lengths and diffusion coefficient values.