Autocovariance of an MA(1) process
= Autocovariance of an MA(1) process
{title2=$\gamma_0=\sigma^2(1+\theta^2),\quad\gamma_1=\sigma^2\theta$}
Only observations at lag one share a noise term. Thus $\gamma_0=\sigma^2(1+\theta^2)$, $\gamma_{\pm1}=\sigma^2\theta$, and every other lag has zero <covariance>. This tridiagonal finite <covariance> structure makes the <finite-sample innovations of an MA(1) process> particularly simple.