This thesis treats features, properties, utility and performance of the use of bootstrap, a resample techique, in the estimation of a parameter related to long memory in times. Among other things, we estimate the standard deviation of the parameter estimator and define a null hypothesis test for the parameter. With bootstrap, we can get large sample properties from a small sample. It consists of many resamples, with reposition, of the original sample, all with the same size as the original. Long memory can be featured by a small decay of the autocorrelations as the lag tends to infinity. Long memory can be studied by ARIMA (p,d,q) models with the d parameters assuming a fractional value (ARFIMA). This work concerns the use of bootstrap in the estimation of the fractional d parameter of ARFIMA (p,d,q) models.