  Among the most important models for long-range dependent time series is the
class of ARFIMA$(p,d,q)$ (Autoregressive Fractionally Integrated Moving
Average) models. Estimating the long-range dependence parameter $d$ in ARFIMA
models is a well-studied problem, but the literature regarding the estimation
of $d$ in the presence of missing data is very sparse. There are two basic
approaches to dealing with the problem: missing data can be imputed using some
plausible method, and then the estimation can proceed as if no data were
missing, or we can use a specially tailored methodology to estimate $d$ in the
presence of missing data. In this work, we review some of the methods available
for both approaches and compare them through a Monte Carlo simulation study. We
present a comparison among 35 different setups to estimate $d$, under tenths of
different scenarios, considering percentages of missing data ranging from as
few as 10\% up to 70\% and several levels of dependence.
