Estimation of the global regularity of a multifractional Brownian motion

Joachim Lebovits; Mark Podolskij

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arXiv · 1607.02391

Estimation of the global regularity of a multifractional Brownian motion

Joachim Lebovits·Mark Podolskij

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Abstract

This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst function, which is, under weak assumptions, identical to the global regularity index of the path.

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Joachim Lebovits, Mark Podolskij. 2016-07-08. Estimation of the global regularity of a multifractional Brownian motion. https://arxiv.org/abs/1607.02391

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