  Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the
Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of
multifractality in the time series. Series fluctuating according to a qGaussian
distribution, both uncorrelated and correlated in time, are used. For the
uncorrelated series at the border (q=5/3) between the Gaussian and the Levy
basins of attraction asymptotically we find a phase-like transition between
monofractal and bifractal characteristics. This indicates that these may solely
be the specific nonlinear temporal correlations that organize the series into a
genuine multifractal hierarchy. For analyzing various features of
multifractality due to such correlations, we use the model series generated
from the binomial cascade as well as empirical series. Then, within the
temporal ranges of well developed power-law correlations we find a fast
convergence in all multifractal measures. Besides of its practical significance
this fact may reflect another manifestation of a conjectured q-generalized
Central Limit Theorem.
