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On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data

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  • Grech, Dariusz
  • Mazur, Zygmunt

Abstract

We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length L and the correlation coefficient of the linear regression R2 at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range λ is found to change linearly—both with L and R2. We show how this dependence can be generalized to a simple unified model describing the relation λ=λ(L,R2,H) where H (1/2≤H≤1) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately.

Suggested Citation

  • Grech, Dariusz & Mazur, Zygmunt, 2013. "On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2384-2397.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:10:p:2384-2397
    DOI: 10.1016/j.physa.2013.01.049
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    Cited by:

    1. Buonocore, R.J. & Aste, T. & Di Matteo, T., 2016. "Measuring multiscaling in financial time-series," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 38-47.
    2. Lahmiri, Salim, 2015. "Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 130-138.
    3. Zhang, Guofu & Li, Jingjing, 2018. "Multifractal analysis of Shanghai and Hong Kong stock markets before and after the connect program," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 611-622.
    4. Lahmiri, Salim, 2017. "On fractality and chaos in Moroccan family business stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 29-39.
    5. Hasan, Rashid & Mohammad, Salim M., 2015. "Multifractal analysis of Asian markets during 2007–2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 746-761.
    6. Echeverria, J.C. & Rodriguez, E. & Aguilar-Cornejo, M. & Alvarez-Ramirez, J., 2016. "Linear combination of power-law functions for detecting multiscaling using detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 283-293.
    7. Ladislav Kristoufek, 2016. "Power-law cross-correlations estimation under heavy tails," Papers 1602.05385, arXiv.org, revised Apr 2016.
    8. 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.
    9. La Spada Gabriele & Lillo Fabrizio, 2014. "The effect of round-off error on long memory processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 445-482, September.
    10. Gulich, Damián & Baglietto, Gabriel & Rozenfeld, Alejandro F., 2018. "Temporal correlations in the Vicsek model with vectorial noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 590-604.
    11. Kristoufek, Ladislav, 2015. "Finite sample properties of power-law cross-correlations estimators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 513-525.
    12. Derick Quintino & Jessica Campoli & Heloisa Burnquist & Paulo Ferreira, 2020. "Efficiency of the Brazilian Bitcoin: A DFA Approach," IJFS, MDPI, vol. 8(2), pages 1-9, April.
    13. Hasan, Rashid & Mohammed Salim, M., 2017. "Power law cross-correlations between price change and volume change of Indian stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 620-631.
    14. Itami, A.S. & Antonio, F.J. & Mendes, R.S., 2015. "Very prolonged practice in block of trials: Scaling of fitness, universality and persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 82-89.
    15. Cao, Guangxi & Shi, Yingying, 2017. "Simulation analysis of multifractal detrended methods based on the ARFIMA process," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 235-243.
    16. Sidorov, S.P. & Faizliev, A.R. & Balash, V.A. & Korobov, E.A., 2016. "Long-range correlation analysis of economic news flow intensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 205-212.
    17. 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.
    18. Postnikov, Eugene B. & Sokolov, Igor M., 2015. "Robust linear regression with broad distributions of errors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 257-267.

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