Forecasting of time data with using fractional Brownian motion

TL;DR

This paper explores forecasting methods for fractional Brownian motion, introduces a new Hurst exponent estimation technique, and develops a stochastic model for short-term time series prediction, validated through software implementation.

Contribution

A novel approach for estimating the Hurst exponent and a stochastic model for fractional Brownian motion are proposed and validated for improved time series forecasting.

Findings

Validated new Hurst exponent estimation method

Developed a stochastic model for fractional Brownian motion

Implemented forecasting tools in software

Abstract

We investigated the quality of forecasting of fractional Brownian motion, and new method for estimating of Hurst exponent is validated. Stochastic model of the time series in the form of converted fractional Brownian motion is proposed. The method of checking the adequacy of the proposed model is developed and short-term forecasting for temporary data is constructed. The research results are implemented.in software tools for analysis and modeling of time series.