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Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

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  • Ying-Hui Shao

    (ECUST)

  • Gao Feng Gu

    (ECUST)

  • Zhi-Qiang Jiang

    (ECUST)

  • Wei-Xing Zhou

    (ECUST)

  • Didier Sornette

    (ETH Zurich)

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    Abstract

    Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.

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    File URL: http://arxiv.org/pdf/1208.4158
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1208.4158.

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    Date of creation: Aug 2012
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    Publication status: Published in Scientific Reports 2, 835 (2012)
    Handle: RePEc:arx:papers:1208.4158

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    Web page: http://arxiv.org/

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    Cited by:
    1. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    2. Ladislav Kristoufek, 2013. "Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series," Papers 1311.0657, arXiv.org.
    3. Jian Zhou & Gao-Feng Gu & Zhi-Qiang Jiang & Xiong Xiong & Wei Zhang & Wei-Xing Zhou, 2014. "Microscopic determinants of the weak-form efficiency of an artificial order-driven stock market," Papers 1404.1051, arXiv.org.
    4. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    5. Zhi-Qiang Jiang & Wen-Jie Xie & Wei-Xing Zhou, 2012. "Testing the weak-form efficiency of the WTI crude oil futures market," Papers 1211.4686, arXiv.org.
    6. Gao-Feng Gu & Xiong Xiong & Yong-Jie Zhang & Wei Chen & Wei Zhang & Wei-Xing Zhou, 2014. "Stylized facts of price gaps in limit order books: Evidence from Chinese stocks," Papers 1405.1247, arXiv.org.

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