Time Series Analysis: Forecasting and Control, Fourth Edition

PART TWO

Stochastic Model Building

We have seen that an ARIMA model of order (p,d,q) provides a class of models capable of representing time series that, although not necessarily stationary, arr homogeneous and in statistical equilibrium in many respects.

The ARIMA model is defined by the equation

where ϕ(B) and θ(B) are operators in B of degree p and q, respectively, whose zeros lie outside the unit circle. We have noted that the model is very general, subsuming autoregressive models, moving average models, mixed autoregressive-moving average models, and the integrated forms of all three.

Iterative Approach to Model Building The relating of a model of this kind to data is usually best achieved by a three-stage iterative procedure based on identification, estimation, and diagnostic checking.

1. By identification we mean the use of the data, and of any information on how the series was generated, to suggest a subclass of parsimonious models worthy to be entertained.
2. By estimation we mean efficient use of the data to make inferences about the parameters conditional on the adequacy of the model entertained.
3. By diagnostic checking we mean checking the fitted model in its relation to the data with intent to reveal model inadequacies and so to achieve model improvement.

In Chapter 6, which follows, we discuss model identification, in Chapter 7 estimation of parameters, and in Chapter ...