Estimation of the fractionally integrated process with Missing Values: Simulation and Application

Time series with long-memory behavior have recently received much attention. Much interest attaches to parameter estimation in the ARFIMA model by considering different situations of this process, and specifically when there are missing observations. This is the focus of this paper. To estimate the parameters of the ARFIMA model, parametric and semiparametric approaches are considered. The way the missing values are distributed can affect the performance of these estimators. We consider two ways for the generating the missing observations: random and block. We also consider innovations that are not normally distributed. The results are obtained through Monte Carlo simulation and a real data set is used to illustrate the methodology