Missing observations in ARIMA models: skipping strategy versus additive outlier approach

Abstract

Optimal estimation of missing values in ARMA models is typically performed by using the Kalman Filter for likelihood evaluation, "skipping" in the computations the missing observations, obtaining the maximum likelihood (ML) estimators of the model parameters, and using some smoothing algorithm. The same type of procedure has been extended to nonstationary ARIMA models in G6mez Maravall (1994). An alternative procedure suggests filling in the holes in the series with arbitrary values and then performing ML estimation of the ARIMA model with Additive Outliers (AO). When the model parameters are not known the two methods differ, since the AO likelihood is affected by the arbitrary values. We develop the proper likelihood for the AO approach in the general non-stationary case and show the equivalence of this and the skipping method. Computationally efficient ways to apply both procedures, based on an Augmented Kalman Filter, are detailed. Finally, the two methods are compared through simulation, and their relative advantages assessed; the comparison also includes the AO method with the uncorrected likelihood.