The selection and use of linear and bilinear time series models

This paper is concerned with problems associated with employing linear and bilinear processes to represent time series phenomena. It contains some discussion of theoretical reasons why bilinear models may prove to be useful for modelling non-Gaussian time series. Attention is paid to the effects of adopting a Bayesian stance to the use of model selection criteria when approaching the question of determining suitable parameterizations. These ideas are illustrated using a familiar data set and their ramifications for forecasting are explored. It transpires in this instance that the one-step ahead forecasts with the smallest mean squared error are generated by a noval combination of the two classes of models entertained.