Blocks adjustment -- reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation
arXiv:0708.1628 · doi:10.1016/j.physa.2007.08.018
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<=H< 1.
20 pages, 14 figures, accepted for publication in Physica A: August 9, 2007