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Bootstrap testing for detrended fluctuation analysis


  • Grau-Carles, Pilar


Detrended fluctuation analysis (DFA) is a scaling method that allows the detection of long memory in a time series. Until now no asymptotic distribution has been found for this statistic. The bootstrap technique allows the simulation of the probability distribution of any statistic. In this paper the results of the Monte Carlo study using bootstrap method show that the DFA test has reasonably good power for short time series. Another advantage of the bootstrap technique is that allows the calculation of finite sample critical values. As an example we calculate bootstrap p-values for financial returns time series using DFA.

Suggested Citation

  • Grau-Carles, Pilar, 2006. "Bootstrap testing for detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 89-98.
  • Handle: RePEc:eee:phsmap:v:360:y:2006:i:1:p:89-98
    DOI: 10.1016/j.physa.2005.05.074

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    Cited by:

    1. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    2. Lin, Xiaoqiang & Fei, Fangyu, 2013. "Long memory revisit in Chinese stock markets: Based on GARCH-class models and multiscale analysis," Economic Modelling, Elsevier, vol. 31(C), pages 265-275.
    3. Cajueiro, Daniel O. & Tabak, Benjamin M., 2010. "Fluctuation dynamics in US interest rates and the role of monetary policy," Finance Research Letters, Elsevier, vol. 7(3), pages 163-169, September.
    4. Wang, Yudong & Wu, Chongfeng & Wei, Yu, 2011. "Can GARCH-class models capture long memory in WTI crude oil markets?," Economic Modelling, Elsevier, vol. 28(3), pages 921-927, May.
    5. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo, 2008. "Short-term predictability of crude oil markets: A detrended fluctuation analysis approach," Energy Economics, Elsevier, vol. 30(5), pages 2645-2656, September.
    6. Gwo-Fong Lin & Ming-Jui Chang & Jyue-Ting Wu, 2017. "A Hybrid Statistical Downscaling Method Based on the Classification of Rainfall Patterns," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(1), pages 377-401, January.
    7. Alvarez-Ramirez, J. & Escarela-Perez, R. & Espinosa-Perez, G. & Urrea, R., 2009. "Dynamics of electricity market correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2173-2188.
    8. Cajueiro, Daniel O. & Tabak, Benjamin M., 2008. "Testing for long-range dependence in world stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 918-927.
    9. Alvarez-Ramirez, Jose & Escarela-Perez, Rafael, 2010. "Time-dependent correlations in electricity markets," Energy Economics, Elsevier, vol. 32(2), pages 269-277, March.
    10. Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
    11. Cajueiro, Daniel O. & Tabak, Benjamin M., 2009. "Testing for long-range dependence in the Brazilian term structure of interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1559-1573.


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