New Algorithmic Developments for Estimation Problems in Time Series
Craig F. Ansley, Robert Kohn · 1984
New filtering results are described for a nonstationary ARIMA model having any pattern of missing data. These results are based on a modification of the Kalman filter which allows the initial state vector to partially diffuse. The problem of defining a likelihood for a nonstationary ARIMA process is discussed, and several alternative approaches are shown to be equivalent. The modified Kalman filter is then used to compute the likelihood. Computational savings arising from the special structure of the Kalman filter conditional covariance matrices are discussed, and different state space representations are compared.