Analysis of fractional Gaussian noises using level crossing method

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.

12 pages, 6 figures and 1 table

References in corpus (1)

• Level Crossing Analysis of Cosmic Microwave Background Radiation: A method for detecting cosmic strings

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