Missing observations in ARIMA models: Skipping strategy versus outlier approach.

The problem of optimal estimation of missing observations in stationary Autoregressive Moving Average (ARMA) models was solved in Jones (1980). Extension of his aproach to nonstationary integrated ARMA (i.e., ARIMA) models posed serious problems, having mostly' to do with the specification of the starting conditions for the Kalman filter and the definition of a. proper likelihood. Several solutions have been proposed, among them, the "transformation" approach of Kohn and Ansley (1986), the "diffuse prior" approach of De Jong (1991), and the "conditional1ikelihood" approach of Gomez and Maravail (1994). These solutions share the basic features of the approach in Jones: the use of (some version of) the Kalman Filter (KF) for likelihood evaluation, "skipping" in the computations the missing observations. Maximum likelihood estimation of the AruMA parameters is then possible, and some smoothing algorithm, such as the Fixed Point Smoother (FPS), interpolates the missing values. We shall refer to this general approach as the "skipping approach". Since the Kohn-Ansley, De Jong, and G6mez-Maravall approaches are equivalent, due to its simplicity, we shall use the latter to represent the skipping approach method.