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：基于多重分形去趋势波动分析（MFDFA）框架内的数学论证，表明在属于高斯吸引域的无相关时间序列中，当序列长度增加时，类似多重分形性的效应对于正阶矩会渐近消失。这一结论同样适用于负阶矩，并可扩展至Lévy稳定涨落区域。相关效应亦通过数值模拟得到验证与佐证。这证明时间序列中的真实多重分形性只能源于长程时间相关性，且仅当存在此类相关性时，涨落的更厚分布尾部才会拓宽奇异谱宽度。因此，关于“时间序列中的多重分形性是由时间相关性还是宽分布尾部引起”这一常见问题本身便存在不当之处。在无相关性的情况下，仅存在双分形或单分形情形：前者对应Lévy稳定涨落区域，后者则属于中心极限定理意义下的高斯吸引域涨落。