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Blocks adjustment – reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation

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  • Sebastian Michalski

    (Department of Applied Econometrics, Warsaw School of Economics)

Abstract

The length of minimal and maximal blocks equally distant on log-log scale versus fluctuation function considerably influences bias and variance of DFA. Through a number of extensive Monte Carlo simulations and different fractional Brownian motion/fractional Gaussian noise generators, we found the pair of minimal and maximal blocks that minimizes the sum of mean-squared error of estimated Hurst exponents for the series of length N = 2^p, p = 7, . . . , 15. Sensitivity of DFA to sort-range correlations was examined using ARFIMA(p, d, q) generator. Due to the bias of the estimator for anti-persistent processes, we narrowed down the range of Hurst exponent to 1/2 =

Suggested Citation

  • Sebastian Michalski, 2006. "Blocks adjustment – reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Working Papers 15, Department of Applied Econometrics, Warsaw School of Economics.
    • Handle: RePEc:wse:wpaper:15
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    File URL: http://kolegia.sgh.waw.pl/pl/KAE/struktura/IE/struktura/ZES/Documents/Working_Papers/aewp08-06.pdf
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    References listed on IDEAS

    as
    1. Raymond, Gary M. & Bassingthwaighte, James B., 1999. "Deriving dispersional and scaled windowed variance analyses using the correlation function of discrete fractional Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(1), pages 85-96.
    2. Coeurjolly, Jean-Francois, 2000. "Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i07).
    3. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
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    1. 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.

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