  Based on the mathematical arguments formulated within the Multifractal
Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the
uncorrelated time series from the Gaussian basin of attraction the effects
resembling multifractality asymptotically disappear for positive moments when
the length of time series increases. A hint is given that this applies to the
negative moments as well and extends to the L\'evy stable regime of
fluctuations. The related effects are also illustrated and confirmed by
numerical simulations. This documents that the genuine multifractality in time
series may only result from the long-range temporal correlations and the fatter
distribution tails of fluctuations may broaden the width of singularity
spectrum only when such correlations are present. The frequently asked question
of what makes multifractality in time series - temporal correlations or broad
distribution tails - is thus ill posed. In the absence of correlations only the
bifractal or monofractal cases are possible. The former corresponds to the
L\'evy stable regime of fluctuations while the latter to the ones belonging to
the Gaussian basin of attraction in the sense of the Central Limit Theorem.
