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：长距离依赖时间序列最重要的模型是ARIFIMA$(p,d,q)(自动递减分数综合移动平均值)模型。在ARFIMA模型中估算长距离依赖性参数(d美元)是一个研究周详的问题,但有关在缺少数据的情况下估算美元值的文献非常稀少。有两种基本的方法来处理这一问题:可用某种合理的方法估算缺失的数据,然后可以进行估算,就像没有缺少数据一样,或者我们可以使用一种专门定制的方法在缺少数据的情况下估算美元值。在这项工作中,我们审查了两种方法中可用的一些方法,并通过蒙特卡洛模拟研究进行比较。我们比较了35种不同的设置和估计美元值,低于不同假设的十分之一,考虑到缺失数据的百分比从10-70-和几个依赖水平不等。</s>