In this paper, we develop the multifractal detrending weighted average algorithm of historical volatility (MF-DHV) for one-dimensional multifractal measure based on the classical multifractal detrended fluctuation analysis (MF-DFA). In the calculation process of getting a local trend for MF-DHV, historical volatility is taken to develop an moving average algorithm, which is different from the simple moving average function in multifractal detrended moving average (MF-DMA). We assess the performance of three methods such as MF-DFA, MF-DMA, and MF-DHV based on the p-model multiplicative cascading constructed time series. The computational results show that all the estimated generalized Hurst exponent H(q), the scaling exponent τ(q), and the singularity spectrum f(α) of MF-DHV are in good agreement with the theoretical values. In addition, we also calculate the standard deviations of Herr and τerr for three methods, and the lowest errors in MF-DHV provides the most accurate estimates. To avoid the accidental selection of parameters, we change the total length of the generated multifractal simulation data and p-value, respectively. It is found that in all the cases, the MF-DHV outperforms the other two methods.

中文翻译：

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历史波动率去趋势加权平均算法的多分形分析

在本文中，我们基于经典的多重分形去趋势波动分析（MF-DFA）开发了一维多重分形度量的历史波动率的多重分形去趋势加权平均算法（MF-DHV）。MF-DHV在获取局部趋势的计算过程中，采用历史波动率开发移动平均算法，不同于多重分形去趋势移动平均（MF-DMA）中的简单移动平均函数。我们评估了三种方法的性能，例如 MF-DFA、MF-DMA 和 MF-DHV，基于p-model 乘法级联构造的时间序列。计算结果表明，所有估计的广义 Hurst 指数H(q), 缩放指数τ(q), 和奇点谱F(α)MF-DHV 与理论值吻合较好。此外，我们还计算了标准差H呃和τ呃对于三种方法，MF-DHV 中的最低误差提供了最准确的估计。为了避免参数的意外选择，我们改变了生成的多重分形模拟数据的总长度和p-值，分别。发现在所有情况下，MF-DHV 都优于其他两种方法。