6Autoregressive and Moving Average Processes
Statements about parameter values have been discussed as if parameters have a clearly‐defined tangible existence, whereas in most cases, they are at best mathematical artifacts introduced only in order to provide the most useful approximation available to the behaviour of the underlying reality. It is all too easy to lose sight of the fact that the real purpose of the analysis is to make statements about this reality rather than about the models that approximate it.
(James Durbin, 1987, p. 179)
There are many extensions of the AR(1) model, a very natural one of which is to include more lagged terms, yielding the AR(
) model. Another important one is to consider lags of the error term 
, giving rise to moving average, or MA(
), models. In this chapter, these two models will be introduced and methods for their estimation discussed.
6.1 AR(
) Processes
A natural generalization of the AR(1) model (4.1) is to allow more past values of 
into the equation; ...
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