Applying the IR statistic to estimate the Hurst index of the fractional geometric Brownian motion
Articles
Dimitrij Melichov
Vilnius Gediminas Technical University
Published 2010-12-21
https://doi.org/10.15388/LMR.2010.67
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Keywords

increment ratio statistic
fractional geometric Brownian motion
fractional Black– Scholes model
Hurst index estimation

How to Cite

Melichov D. (2010) “Applying the IR statistic to estimate the Hurst index of the fractional geometric Brownian motion”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 368–372. doi: 10.15388/LMR.2010.67.

Abstract

In 2010 J.M. Bardet and D. Surgailis [1] have introduced the increment ratio (IR) statistic which measures the roughness of random paths. It was shown that this statistic was applicable in the cases of diffusion processes driven by the standard Brownian motion, certain Gaussian processes and the Lévy process. This paper shows that the IR statistic can be applied to estimate the Hurst index H of the fractional geometric Brownian motion.

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