  Correlation analysis is convenient and frequently used tool for investigation
of time series from complex systems. Recently new methods such as the
multifractal detrended fluctuation analysis (MFDFA) and the wavelet transform
modulus maximum method (WTMM) have been developed. By means of these methods
(i) we can investigate long-range correlations in time series and (ii) we can
calculate fractal spectra of these time series. But opposite to the classical
tool for correlation analysis - the autocorrelation function, the newly
developed tools are not applicable to all kinds of time series. The
unappropriate application of MFDFA or WTMM leads to wrong results and
conclusions. In this article we discuss the opportunities and risks connected
to the application of the MFDFA method to time series from a random number
generator and to experimentally measured time series (i) for accelerations of
an agricultural tractor and (ii) for the heartbeat activity of {\sl Drosophila
melanogaster}. Our main goal is to emphasize on what can be done and what can
not be done by the MFDFA as tool for investigation of time series.
