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arXiv · 1112.1502

Analysis of fractional Gaussian noises using level crossing method

M. Vahabi·G. R. Jafari·M. Sadegh Movahed
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Abstract

The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic series could be a suitable benchmark to make the level crossing findings more sense. In this article, we calculated the average frequency of upcrossing for a wide range of fractional Gaussian noises from logarithmic (zero Hurst exponent, H=0), to Gaussian, H=1, ($0<H<1$). By introducing the relative change of the total numbers of upcrossings for original data with respect to so-called shuffled one, $\mathcal{R}$, an empirical function for the Hurst exponent versus $\mathcal{R}$ has been established. Finally to make the concept more obvious, we applied this approach to some financial series.

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M. Vahabi, G. R. Jafari, M. Sadegh Movahed. 2011-12-07. Analysis of fractional Gaussian noises using level crossing method. https://doi.org/10.1088/1742-5468%2F2011%2F11%2Fp11021

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