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.

翻译：长程依赖时间序列中最重要的模型之一是ARFIMA$(p,d,q)$（自回归分数整合移动平均）模型。在ARFIMA模型中估计长程依赖参数$d$是一个经过充分研究的问题，但关于缺失数据情况下估计$d$的文献却非常稀少。处理该问题有两种基本方法：可以基于某种合理方法对缺失数据进行插值，然后像没有数据缺失一样进行估计，或者采用专门定制的统计方法在存在缺失数据时估计$d$。本文综述了两种方法中的若干可用技术，并通过蒙特卡洛模拟研究进行了比较。我们在数十种不同场景下，针对缺失数据比例从低至10%到高达70%以及多个依赖水平，展示了35种不同设置下估计$d$的比较结果。