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The exact likelihood function for a mixed autoregressive-moving average process

1974; Oxford University Press; Volume: 61; Issue: 3 Linguagem: Inglês

10.1093/biomet/61.3.423

1464-3510

Paul Newbold,

Forecasting Techniques and Applications

Box & Jenkins (1970) develop a strategy for the analysis and forecasting of time series, based on the construction, after suitable differencing, of autoregressive-moving average models. They present a model building procedure which works very well for most general purposes, and in addition derive the exact likelihood function for both pure autoregressive and pure moving average processes, in the latter case this being a new result. In this note it is shown that a similar approach can be employed to derive the exact likelihood function for the mixed process.