# Stationary Process versus limit of MA(q)

The Wold representation says that any stationary process is equivalent to a MA($\infty$) process which, in turn, is the limit of a MA(q) process. Does that mean that anything that can be proved for an MA(q) immediately generalizes to any stationary process? I suspect this is not the case. but can't really come up with a counter-example.

• For the process to be stationary there are conditions on the moving average parameters. – Michael R. Chernick Feb 6 '17 at 22:26

Proposition. Let $y_t$ be a series from $MA(q)$. Then for any $q$, there is $s$ such that $Cov(y_t,y_{t-s})=0$.
Obviously, the above proposition is true. But there is no such $s$ for $AR(1)$ process with non-zero AR coefficient.
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