英文标题：
《Direct determination approach for the multifractal detrending moving
  average analysis》
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作者：
Hai-Chuan Xu, Gao-Feng Gu and Wei-Xing Zhou (ECUST)
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最新提交年份：
2019
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英文摘要：
  In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent $\\tau(q)$ is related to the partition function and the multifractal spectrum $f(\\alpha)$ can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional $p$-model, the two-dimensional $p$-model and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum $f(\\alpha)$ can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.
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中文摘要：
在规范框架下，我们提出了一种基于去趋势移动平均法（MF-DMA）的多重分形分析方法。我们定义了一个正则测度，使得多重分形质量指数$\\ tau（q）$与配分函数相关，并且可以直接确定多重分形谱$\\ f（\\ alpha）$。基于由一维$p$模型、二维$p$模型和分数布朗运动生成的三种综合多重分形和单分形测度，比较了MF-DMA的直接确定方法和传统方法的性能。我们发现，这两种方法在揭示分形和多重分形性质方面具有可比性。换言之，在不损失精度的情况下，可以使用新方法直接确定多重分形谱$f（\\α）$，且计算成本较低。我们还将新的MF-DMA方法应用于股票价格的波动时间序列，并确认了多重分形的存在。
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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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