MA(q) ACF Cutoff Property
Theorem
For an MA(q) process, the theoretical ACF satisfies:
$$\rho(h) = 0, \qquad \forall |h| > q$$The ACF cuts off (becomes exactly zero) after lag $q$. MA(q) is therefore also called a $q$-correlated process.
Model Identification Use
If the sample ACF plot shows significant values at lags $1, \ldots, q$ and drops to ~0 (within $\pm 1.96/\sqrt{n}$ bounds) for $h > q$, this suggests an MA(q) model.