Mariani Maria C, Kubin William, Asante Peter K, Guthrie Joe A, Tweneboah Osei K
Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79902, USA.
Computational Science Program, University of Texas at El Paso, El Paso, TX 79902, USA.
Entropy (Basel). 2021 Nov 13;23(11):1505. doi: 10.3390/e23111505.
In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.
在本文中，我们使用三元康托集对去趋势波动分析（DFA）进行了改进。我们提出了一种DFA算法的改进版本，即康托DFA（CDFA），它将以3为底的康托集理论用作DFA算法中分段大小的尺度。我们还基于康托集理论，对使用真实世界时间序列的证明所产生的现象进行了研究。通过将这种新方法与截断列维飞行（TLF）的α的反比关系进行比较，有助于减少DFA的赫斯特指数的高估问题。CDFA还能够正确预测时间序列的记忆行为。
