Estimation of Long-Range Dependent Models with Missing Data: to Input or not to Input?
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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.
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