The AR process just discussed is not the only mechanism that may have generated Y. Suppose we model Y as follows:
where v is a constant and u, as before, is the white noise stochastic error term. Here Y at time t is equal to a constant plus a moving average of the current and past error terms. Thus, in the present case, we say that Y follows a first-order moving average, or an MA(1), process. But if Y follows the expression
then it is an MA(2) process. More generally,
Yt = V + PoUt + PiUt-i + P2Ut-2 +-----+ PqUt-q (22.2.6)
is an MA(q) process. In short, a moving average process is simply a linear combination of white noise error terms.
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