Time Series Analysis: Forecasting and Control, Fourth Edition

PART THREE

Transfer Function and Multivariate Model Building

Suppose that X measures the level of an input to a dynamic system. For example, X might be the concentration of some constituent in the feed to a chemical process. Suppose that the level of X influences the level of a system output Y. For example, Y might be the yield of product from the chemical process. It will usually be the case that because of the inertia of the system, a change in X from one level to another will have no immediate effect on the output but, instead, will produce delayed response with Y eventually coming to equilibrium at a new level. We refer to such a change as a dynamic response. A model that describes this dynamic response is called a transfer function model. We shall suppose that observations of input and output are made at equispaced intervals of time. The associated transfer function model will then be called a discrete transfer function model.

Models of this kind can describe not only the behavior of industrial processes but also that of economic and business systems. Transfer function model building is important because it is only when the dynamic characteristics of a system are understood that intelligent direction, manipulation, and control of the system is possible.

Even under carefully controlled conditions, influences other than X will affect Y. We refer to the combined effect on Y of such influences as the disturbance or the noise. A model such as can be related to real data must take ...