摘要翻译：
本文利用多重分形离散波动分析(MFDFA)分别对德国DAX30指数的正向和负向变化进行了分形分析。通过计算奇异谱$f(\alpha)$，我们发现这两个符号的返回都显示了多尺度性。奇怪的是，这些谱显示了具有相反符号的回报的标度性质的显著差异。负的价格变化比正的价格变化具有更强的时间相关性，这表现在相应的h\\{o}lder指数的更大值上。就主导趋势的性质而言，熊市比牛市更持久，而不考虑波动的迹象。
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英文标题：
《Different fractal properties of positive and negative returns》
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作者：
P. Oswiecimka, J. Kwapien, S. Drozdz, A. Z. Gorski, R. Rak
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最新提交年份：
2008
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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：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  We perform an analysis of fractal properties of the positive and the negative changes of the German DAX30 index separately using Multifractal Detrended Fluctuation Analysis (MFDFA). By calculating the singularity spectra $f(\alpha)$ we show that returns of both signs reveal multiscaling. Curiously, these spectra display a significant difference in the scaling properties of returns with opposite sign. The negative price changes are ruled by stronger temporal correlations than the positive ones, what is manifested by larger values of the corresponding H\"{o}lder exponents. As regards the properties of dominant trends, a bear market is more persistent than the bull market irrespective of the sign of fluctuations.
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PDF链接：
https://arxiv.org/pdf/0803.1374