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Performance of multifractal detrended fluctuation analysis on short time series

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  • Juan Luis Lopez
  • Jesus Guillermo Contreras

Abstract

The performance of the multifractal detrended analysis on short time series is evaluated for synthetic samples of several mono- and multifractal models. The reconstruction of the generalized Hurst exponents is used to determine the range of applicability of the method and the precision of its results as a function of the decreasing length of the series. As an application the series of the daily exchange rate between the U.S. dollar and the euro is studied.

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  • Juan Luis Lopez & Jesus Guillermo Contreras, 2013. "Performance of multifractal detrended fluctuation analysis on short time series," Papers 1311.2278, arXiv.org.
    • Handle: RePEc:arx:papers:1311.2278
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    1. Kristjanpoller, Werner & Bouri, Elie & Takaishi, Tetsuya, 2020. "Cryptocurrencies and equity funds: Evidence from an asymmetric multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Telesca, Luciano & Haro-Pérez, Catalina & Moreno-Torres, L. Rebeca & Ramirez-Rojas, Alejandro, 2018. "Multifractal detrended fluctuation analysis of intensity time series of photons scattered by tracer particles within a polymeric gel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 994-1003.
    3. Ferreira, Paulo, 2018. "Long-range dependencies of Eastern European stock markets: A dynamic detrended analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 454-470.
    4. Sarker, Alivia & Mali, Provash, 2021. "Detrended multifractal characterization of Indian rainfall records," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    5. da Silva Filho, Antônio Carlos & Maganini, Natália Diniz & de Almeida, Eduardo Fonseca, 2018. "Multifractal analysis of Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 954-967.
    6. López, J.L. & Veleva, L., 2022. "2D-DFA as a tool for non-destructive characterisation of copper surface exposed to substitute ocean water," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    7. Wu, Liang & Chen, Lei & Ding, Yiming & Zhao, Tongzhou, 2018. "Testing for the source of multifractality in water level records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 824-839.
    8. Sierra-Porta, D., 2024. "A multifractal approach to understanding Forbush Decrease events: Correlations with geomagnetic storms and space weather phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    9. 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.
    10. Hongli Niu & Jun Wang, 2014. "Phase and multifractality analyses of random price time series by finite-range interacting biased voter system," Computational Statistics, Springer, vol. 29(5), pages 1045-1063, October.
    11. Guan, Sihai & Wan, Dongyu & Yang, Yanmiao & Biswal, Bharat, 2022. "Sources of multifractality of the brain rs-fMRI signal," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    12. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    13. Telesca, Luciano & Toth, Laszlo, 2016. "Multifractal detrended fluctuation analysis of Pannonian earthquake magnitude series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 21-29.
    14. Ferreira, Paulo, 2018. "What detrended fluctuation analysis can tell us about NBA results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 92-96.
    15. Paulo Ferreira, 2020. "Dynamic long-range dependences in the Swiss stock market," Empirical Economics, Springer, vol. 58(4), pages 1541-1573, April.
    16. Telesca, Luciano & Lovallo, Michele & Kanevski, Mikhail, 2016. "Power spectrum and multifractal detrended fluctuation analysis of high-frequency wind measurements in mountainous regions," Applied Energy, Elsevier, vol. 162(C), pages 1052-1061.
    17. Fernandes, Leonardo H.S. & de Araújo, Fernando H.A. & Silva, Igor E.M., 2020. "The (in)efficiency of NYMEX energy futures: A multifractal analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    18. Zhang, Rui & Jia, Cairang & Wang, Jian, 2022. "Text emotion classification system based on multifractal methods," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    19. Kristjanpoller, Werner & Nekhili, Ramzi & Bouri, Elie, 2024. "Blockchain ETFs and the cryptocurrency and Nasdaq markets: Multifractal and asymmetric cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    20. Ferreira, Paulo & Dionísio, Andreia & Guedes, Everaldo Freitas & Zebende, Gilney Figueira, 2018. "A sliding windows approach to analyse the evolution of bank shares in the European Union," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1355-1367.

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