Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting

This paper explores the capabilities of machine learning for probabilistic forecasting fractional Brownian motion (fBm). The focus is on predicting probability value an fBm time series exceeding a certain threshold after specific number steps, given only knowledge its Hurst exponent. study aims to determine if self-similarity property preserved in and which algorithms are most effective. Two types methods investigated: with predefined distribution shape those without. results show that self-similar properties can be reliably reproduced continuations predicted by methods. also provides experimental comparison various their potential applications analysis modeling fractal series.