论文标题
时间序列中的真正多纹理是由于时间相关性
Genuine multifractality in time series is due to temporal correlations
论文作者
论文摘要
基于在多重二次降解波动分析（MFDFA）方法中提出的数学参数，这表明，在吸引吸引的高斯盆地的不相关时间序列中，当时间序列的长度增加时，类似于多种裂纹的效果类似于多乳突的效果。提示这也适用于负矩，并扩展到lévy稳定的波动状态。相关效果还通过数值模拟说明和确认。该文件表明，时间序列中真正的多纹理性只能源于远程时间相关性和波动的额外分布尾巴，只有在存在此类相关性时，才能拓宽奇异性光谱的宽度。因此，是什么使时间序列中的多重纹理（时间相关性或广泛的分布尾巴）的常见问题出现。在没有相关性的情况下，只有两性或单一病例。前者对应于lévy稳定的波动状态，而后者则与属于中心极限定理意义上的高斯吸引力盆地相对应。
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 Lévy 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 Lévy 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.
