Time Series Analysis: Forecasting and Control, Fourth Edition

CHAPTER TWELVE

Identification, Fitting, and Checking of Transfer Function Models

In Chapter 11 a parsimonious class of discrete linear transfer function models was introduced:

or

In these models X_t and Y_t were deviations from equilibrium of the system input and output. In practice the system will be infected by disturbances, or noise, whose net effect is to corrupt the output predicted by the transfer function model by an amount N_t. The combined transfer function–noise model may then be written as

In this chapter, methods are described for identifying, fitting, and checking transfer function–noise models when simultaneous pairs of observations (X₁, Y₁), (X₂, Y₂), …, (X_N, Y_N) of the input and output are available at discrete equispaced times 1, 2, …, N.

Engineering methods for estimating transfer functions are usually based on the choice of special inputs to the system, for example, step and sine wave inputs [316] and “pulse” inputs [161]. These methods have been useful when the system is affected by small amounts of noise but are less satisfactory otherwise. In the presence of appreciable noise, it is necessary to use statistical methods for estimating the transfer function. ...