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英文标题：
《Multifractal Flexibly Detrended Fluctuation Analysis》
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作者：
Rafal Rak, Pawel Zi\\k{e}ba
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最新提交年份：
2015
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英文摘要：
Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation Analysis (MFDFA). However, it has some drawback. One of its core elements is detrending of the series. In the classical MFDFA a trend is estimated by fitting a polynomial of degree $m$ where $m=const$. We propose that the degree $m$ of a polynomial was not constant ($m\\neq const$) and its selection was ruled by an established criterion. Taking into account the above amendment, we examine the multifractal spectra both for artificial and real-world mono- and the multifractal time series. Unlike classical MFDFA method, obtained singularity spectra almost perfectly reflects the theoretical results and for real time series we observe a significant right side shift of the spectrum.
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中文摘要：
多重分形时间序列分析是一种显示系统可能复杂性的方法。目前，确定多重分形特征的最流行和最好的方法之一是多重分形去趋势波动分析（MFDFA）。然而，它也有一些缺点。它的核心元素之一是对该系列的贬损。在经典的MFDFA中，趋势是通过拟合一个度为$m$的多项式来估计的，其中$m=const$。我们认为多项式的阶数$m$不是常数（$m\\neq const$），它的选择由一个既定的标准决定。考虑到上述修正，我们研究了人工和真实世界的单分形和多重分形时间序列的多重分形谱。与经典的MFDFA方法不同，获得的奇异谱几乎完美地反映了理论结果，对于实时序列，我们观察到谱的显著右移。
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Physics 物理学
二级分类：Data Analysis, Statistics and Probability 数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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