Forecasting of time data with using fractional Brownian motion

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

Computational technique for simulating variable-order fractional Heston model with application in US stock market

“…In the last decades, the theory of fractional calculus was motivated as a useful mathematical tool to handle application of associated concepts in the areas of physics, chemistry, economics, finance and engineering sciences [23][24][25][26][27][28][29][30][31][32][33][34]. To the author's best knowledge, while numerous stochastic volatility models driven by fractional Brownian motion have been considered [35][36][37][38], stochastic volatility models with fixed-order and variable-order fractional derivative operators have not been carried out and this topic is far from being fully explored. More recently, just a numerical discretization technique has been proposed for approximation of a class of fractional stochastic differential equations driven by Brownian motion [39].…”