A State-Space Approach to Transfer-Function Modeling

The state-space formulation allows model selection using the AIC criterion and the analysis of data with missing values in either or both of the input and output series. An extension of the argument is used to analyze a generalized transfer-function model in which dependence is allowed between the input and output noise sequences. The results are illustrated with reference to the Leading Indicator Sales Data of Box and Jenkins. This chapter discusses the question of parameter estimation and model selection and reanalyzes this example using maximum Gaussian likelihood and the AIC criterion. Before doing so, it shows how the formulation of the model in state-space form facilitates prediction.