Joint multifractality has been studied in many areas of applied sciences, but few studies focused on the sources of joint multifractality, especially the cross-correlations between two records which play a crucial role in the presence of joint multifractality. To test the effect of cross-correlations on joint multifractality, we propose a de-cross-correlation method via the shifting technique based on the framework of multifractal detrended cross-correlation analysis (MF-DCCA), namely, multifractal detrended de-cross-correlation analysis (MF-DDA). It keeps the original detrending procedure of MF-DCCA. The proposed method is validated via some simulation and real data including multifractal random walk (MRW), daily water levels, and daily stock returns. Results of validation show that the MF-DDA can detect the effects of cross-correlations between simulation series and between real series, and are consistent with the simulation setting of MRW and the actual situation of real data. This proposed method can be extended to other similar joint multifractal analysis methods.

中文翻译：

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检验互相关对联合多重分形的影响

联合多重分形已在应用科学的许多领域进行了研究，但很少有研究关注联合多重分形的来源，特别是在联合多重分形的存在中起关键作用的两条记录之间的互相关。为了测试互相关对联合多重分形的影响，我们提出了一种基于多重分形去趋势互相关分析（MF-DCCA）框架的移位技术的去互相关方法，即多重分形去趋势去交叉-相关分析（MF-DDA）。它保留了MF-DCCA的原始去趋势程序。所提出的方法通过一些模拟和真实数据进行了验证，包括多重分形随机游走 (MRW)、每日水位和每日股票收益。验证结果表明，MF-DDA能够检测出模拟序列之间和真实序列之间的互相关效应，与MRW的模拟设置和真实数据的实际情况一致。这种提出的方​​法可以扩展到其他类似的联合多重分形分析方法。