Our goal in this work is to construct empirical confidence intervals for the fractional parameter $d$ in ARFIMA $(0, d, 0)$ processes. Through these confidence intervals one can compare several estimators for d to decide which one is the best estimation method related to long memory time series. We use a fortran routine that simulates random time series to later perform an analysis for detecting long memory. We also apply the methodology to real DNA sequences to evaluate the efficiency of our method in the construction of these confidence intervals.
