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

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.