Optimal Choice for the Numbers of Regressors in the DFA Method

The method of detrended fluctuation analysis has proven useful in revealing the extent of long-range dependence in time series. The objective of this technique is to evaluate the statistical fluctuation F(l) in order to obtain a set of measures, where l represents the window length. By varying the length l, the fluctuation can be characterized by the scaling exponent, that is, the slope coefficient of the line obtained by the regression of ln(F(l)) on ln (l), with l in {4,5,..., g(n)}. Here we carried out simulations of ARFIMA(0,d,0) models, to investigate the effect of g(n) in the detrended fluctuation analysis method. We also analyze the long-range dependence parameter for two DNA sequences with this technique.