Multifractality in time series is due to temporal correlations

Based on the rigorous mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series the effects resembling multifractality asymptotically disappear when the length of time series increases. The related effects are also illustrated 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