小波分析与时间序列的标度性质
Comment on Wavelet Analysis and scaling properties of time series
摘要：
在最近的工作Manimaran等人[Manimaran等人，物理评论E 72，046120（2005）]提出使用多分辨率Daubechies（DB）小波（去趋势）去除低频趋势，随后量化给定时间序列中的多重分形结构。本文将DB小波应用于长程相关数据，指出在线性趋势存在的情况下，小波不能区分相关性和趋势性。由于基于DB小波的去趋势方法不能量化被趋势掩盖的相关性，其多重分形扩展并不总是能得到给定数据的多重分形谱的正确估计。
英文摘要：
In a recent work Manimaran et al. [Manimaran et al., Phys. Rev. E 72, 046120 (2005)] propose to use multiresolution Daubechies (DB) wavelets to (detrend) remove the low frequency trends and subsequently to quantify the multifractal structure in a given time series. In this comment, by applying DB wavelets to the long range correlated data we show that in the presence of linear trends, the wavelets could not able to distinguish the correlations from trends. As the DB wavelets based detrending will not be able to quantify the correlations masked by trends, its multifractal extension can not always yield a correct estimate of the multifractal spectrum of the given data.
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