Time Series Analysis: Forecasting and Control, Fourth Edition

CHAPTER SIX

Model Identification

In this chapter we discuss methods for identifying nonseasonal ARIMA time series models. Identification methods are rough procedures applied to a set of data to indicate the kind of representational model that is worthy of further investigation. The specific aim here is to obtain some idea of the values of p, d, and q needed in the general linear ARIMA model and to obtain initial estimates for the parameters. The tentative model so obtained provides a starting point for the application of the more formal and efficient estimation methods described in Chapter 7.

6.1 OBJECTIVES OF IDENTIFICATION

It should first be said that identification and estimation necessarily overlap. Thus, we may estimate the parameters of a model, which is more elaborate than that which we expect to find, so as to decide at what point simplification is possible. Here we employ the estimation procedure to carry out part of the identification. It should also be explained that identification is necessarily inexact. It is inexact because the question of what types of models occur in practice and in what circumstances, is a property of the behavior of the physical world and therefore cannot be decided by purely mathematical argument. Furthermore, because at the identification stage no precise formulation of the problem is available, statistically “inefficient” methods must necessarily be used. It is a stage at which graphical methods are particularly useful and judgment must be ...