On the estimation of ARIMA Models with Missing Values

The problem of defining a likelihood for a nonstationary ARIMA process is discussed, and several alternative approaches are shown to be equivalent. A new algorithm based on a modification of the Kalman filter is developed to compute the likelihood recursively under any pattern of missing data, including missing starting values. A new state space representation is developed which exploits the covariance structure more efficiently than other representations that have been proposed in the literature.