Missing values in time series can be treated as unknown parameters and estimated by maximum likelihood or as random variables and predicted by the conditional expectation of the unknown values given the data. The purpose of this study is to impute missing values which are regarded as the maximum likelihood estimator and random variable in incomplete data and to compare with two methods using ARMA and STAR model. For illustration, the Mumps data reported from the national capital region monthly over the years 2001~2009 are used, and estimate precision of missing values and forecast precision of future data are compared with two methods.