The estimation of dynamic models with missing observations

Abstract

An ARMA model can be put in state space form and its exact likelihood function calculated by the Kalman filter. The same technique can be extended to handle missing observations, including cases where the data are initially available at an annual level and subsequently become available on a quartely, or monthly, basis. The Kalman filter enables the likelihood function to be computed for both stock and flow data. Once a suitable model has been fitted, the missing observations may be estimated by "smoothing". The paper first sets out the Kalman filter approach to missing observations for an ARMA time series model and discusses the implementation of an efficient algorithm. The results are then extended to cover static regression models with ARMA disturbances and dynamic models. A series of Monte Carlo experiments comparing the efficiency of different estimation procedures are reported.