Two-step prediction for an MA(1) process
= Two-step prediction for an MA(1) process
{title2=$\widehat X_{T+2\mid T}=0$}
In a centered MA(1) process, $X_{T+2}$ is uncorrelated with every observation through time $T$. Its best <linear predictor> from that information is therefore zero, with error <variance> $\sigma^2(1+\theta^2)$. One-step innovation formulas using $X_{T+1}$ cannot be substituted when that observation is unavailable.