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.

翻译：本文基于Multifractal Detrended Fluctuation Analysis（MFDFA）方法中的数学论点，表明在高斯吸引盆地中的非相关时间序列中，当时间序列长度增加时，类似多重分形性的效应渐近消失于正时刻。这提示说，这适用于负时刻，并扩展到波动的L\'evy稳定区域。相关效应还通过数值模拟进行了说明和确认。这证明了在时间序列中真正的多重分形性只可能由长程时间相关性引起，而波动的更加丰富的分布尾巴只有在存在这样的相关性时才会扩展奇异性谱的宽度。在不存在相关性时，人们经常问什么使时间序列的分形性多重化-时间相关性还是广泛的分布尾巴-因此是错误的。在没有相关性的情况下，只有双分形或单分形情况是可能的。前者对应于波动的L\'evy稳定区域，后者对应于遵循中心极限定理的高斯吸引盆地中的波动。