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Vol.2 , No. 1, Publication Date: Feb. 9, 2015, Page: 1-8
| [1] | Said Taan El Hajjar, Department of Mathematical Sciences, Ahlia University, Manama, Kingdom of Bahrain. |
This study aims to learn an estimation of the Hurst Parameter for unevenly sampled fractional Brownian motion. The motions are reproduced by means of Cholesky’s algorithm, and the parameter of Hurst is predicted by maximizing likelihoods. These methods are proven to be suitable for the use of quantitative data utilised in this paper during simulation. Several tables that contain the estimates of the self-similarity measure are presented in this study according to various sampling procedures with various sizes of motions. The initiations of these tables is stood on a sequence of statistical tests based on Student’s t-test and Fisher’s Test that make it possible to analyze and compare the distinctions between the considered sampling processes. This paper deals with the simulation of the fractional Brownian motions, with their identifications, and with the analysis of the experimental results. This study proves that unpredictable sampling gives more inconsistency between the outcomes and those expected values for a balance sampling. This inconsistency has a tendency to be decreased if there is increase in the size of the signals. Also, this study shows that when there is a uniformlyrandom sampling model, outputs from random samplings tend to be similar to those outputs that come from a balance deterministic sampling. It confirms that the best estimators of Hurst’s parameter are obtained by maximizing the chance.
Keywords
Fractional Brownian Motion, Estimation of Hurst Parameter, Unbalanced Sampling, Maximum Likelihood Estimator, Fisher Test, Student’s t- Test
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