Baxter estimates of the Hurst parameter of fractional Brownian motion
DOI:
https://doi.org/10.17721/1812-5409.2019/3.2Abstract
In the paper consistent estimates of the Hurst parameter of fractional Brownian motion are obtained and confidence intervals of the obtained estimates are constructed.
In many applications related to data processing, it is necessary to estimate the Hurst parameter. Among such tasks is the task of signal processing and analysis, when the signal can be considered as the imposition of a useful signal and background noise. Background noise is usually a combination of stochastic and fractal components.
Numerical indicators of these properties are, respectively, the Hurst index, the stability index, the coefficients of the relationship of increments, which generalize the autocorrelation function. Obviously, the estimation of the Hurst index is a priority in the analysis of self-similar processes.
Currently, there are many methods for estimating the Hurst parameter, but they are all focused on individual cases of processes where the property of self-similarity is combined with either long-term dependence (fractional Brownian motion), or with heavy tails.
RS-analysis, disperse-time analysis and deviation analysis are most often used in estimating the Hurst parameter. A common feature of these methods is that they are all based on the use of statistical properties of second-order samples (variance, standard deviation, correlation coefficients).
Key words: Hurst index, fractional Brownian motion, consistent estimate.
Pages of the article in the issue: 18 - 23
Language of the article: Ukrainian
References
KOZACHENKO, Y.V., KURCHENKO, O.O., SYNYAVSKA, O.O. (2018) Levy-Baxter theorems for random fields and their application. Uzgorod: Shark.
KIRICHENKO, L. (2014) Analysis of the properties of ordinary Levy motion based on the estimation of stability index. Information Content and Processing, Vol. 1, Number, pp.170-181.
SHERGIN, V.L. (2013) Estimation of the stability factor of alpha-stable laws using fractional moments method. Eastern-European Journal of Enterprise Technologies, Vol. 6, pp.25-30.
FIHTENGOLZ, G.M. (1968) Fundamentals of Mathematical Analysis. M.: Nauka.
LAMPERTY, D. (1983) Random processes. K.: Vyshcha shkola.
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