  We introduce a particular construction of an autocorrelation matrix of a time
series and its analysis based on the random-matrix theory ideas that is capable
of unveiling the type of correlations information which is inaccessible to the
straight analysis of the autocorrelation function. Exploiting the well-studied
hierarchy of the fractional Gaussian noise (fGn), an \emph{in situ} criterion
for the sake of a quantitative comparison with the autocorrelation data is
offered. We illustrate the applicability of our method by two paradigmatic
examples from the orthodox context of the stock markets and the turbulence.
Quite strikingly, a remarkable agreement with the fGn is achieved
notwithstanding the non-Gaussianity in returns of the stock market. In the
latter context, on the contrary, a significant deviation from an fGn is
observed despite a Gaussian distribution of the velocity profile of the
turbulence.
