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

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  • Michalski, Sebastian

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=2p,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 12⩽H<1.

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  • Michalski, Sebastian, 2008. "Blocks adjustment—reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 217-242.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:1:p:217-242
    DOI: 10.1016/j.physa.2007.08.018
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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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