Tayeb Jamali, Hamed Saberi, G. R. Jafari
We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory (RMT) that is capable of unveiling the type of information about the statistical correlations which is inaccessible to the straight analysis of the autocorrelation function. Exploiting the well-studied hierarchy of the fractional Gaussian noise (fGn), an in situ criterion for the sake of a quantitative comparison with the autocorrelation data is offered. We demonstrate the applicability of our method by two paradigmatic examples from the orthodox context of the turbulence and the stock markets. Quite strikingly, a significant deviation from an fGn is observed despite a Gaussian distribution of the velocity profile of turbulence. In the latter context, on the contrary, a remarkable agreement with the fGn is achieved notwithstanding the non-Gaussianity in returns of the stock market.
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http://arxiv.org/abs/1305.4895
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