On some statistics of fractional Brownian motion

Authors

  • Viktor Bondarenko Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-1663-4799

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2021.1.11

Keywords:

fractional Brownian motion, parameter estimation, statistical hypothesis testing

Abstract

Fractional Brownian motion as a method for estimating the parameters of a stochastic process by variance and one-step increment covariance is proposed and substantiated. The root-mean-square consistency of the constructed estimates has been proven. The obtained results complement and generalize the consequences of limit theorems for fractional Brownian motion, that have been proved in the number of articles. The necessity to estimate the variance is caused by the absence of a base unit of time and the estimation of the covariance allows one to determine the Hurst exponent. The established results let the known limit theorems to be used to construct goodness-of-fit criteria for the hypothesis “the observed time series is a transformation of fractional Brownian motion” and to estimate the error of optimal forecasting for time series.

Author Biography

Viktor Bondarenko, Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Viktor G. Bondarenko, Doctor of Physical and Mathematical Sciences, a professor at the Department of Mathematical Methods of System Analysis of Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

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Published

2021-07-13

Issue

Section

New methods in system analysis, computer science and theory of decision making