Fast filtering for seasonal moving average models

Pearlman (1980) gives a fast filtering algorithm for an ARMA, i.e. autoregressive-moving average, model. When the algorithm is applied to a seasonal moving average model significant computational savings can be obtained by taking advantage of the structural zeros noted by Kohn & Ansley (1984) and Melard (1984). In this paper we identify a second set of structural zeros which leads to further significant computational savings. Our results can be applied to produce a fast algorithm for obtaining the likelihood of a stationary ARMA model with a seasonal moving average.