ABSTRACT
In Chapter 7, we discussed the problem of estimating the parameters of a given ARMA(p,q) process assuming that the model orders p and q are known. The procedure for finding an appropriate model actually begins with the intriguing and sometimes challenging problem of determining the number of parameters that should be estimated. In this chapter, we consider the problem of identifying the model orders p and q of a stationary ARMA(p,q) model as well as p, d, and q for the nonstationary ARUMA(p,d,q) model, and the model orders associated with a multiplicative seasonal model. Since there is realistically not a “true ARMA model” for a real process, our goal will be to find a model that adequately describes the process but does not contain unnecessary parameters. Tukey (1961) refers to such a model as being parsimonious.
