  Correlations in multifractal series have been investigated, extensively.
Almost all approaches try to find scaling features of a given time series.
However, the analysis of such scaling properties has some difficulties such as
finding a proper scaling region. On the other hand, such correlation detection
methods may be affected by the probability distribution function of the series.
In this article, we apply the horizontal visibility graph algorithm to map
stochastic time series into networks. By investigating the magnitude and sign
of a multifractal time series, we show that one can detect linear as well as
nonlinear correlations, even for situations that have been considered as
uncorrelated noises by typical approaches like MFDFA. In this respect, we
introduce a topological parameter that can well measure the strength of
nonlinear correlations. This parameter is independent of the probability
distribution function and calculated without the need to find any scaling
region. Our findings may provide new insights about the multifractal analysis
of time series in a variety of complex systems.
