Two-step prediction for an MA(1) process (${\hat{X}}_{T+2\mid T}=0$)

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.