Odd-subsample long-run variance of a moving average
= Odd-subsample long-run variance of a moving average
{title2=$\frac{\sigma^2}{2}[\Theta(1)^2+\Theta(-1)^2]$}
For coefficients $\theta_0=1,\theta_1,\ldots,\theta_q$, the <long-run variance of a stationary process> sampled every second time is $\sigma^2[(\sum_{j\text{ even}}\theta_j)^2+(\sum_{j\text{ odd}}\theta_j)^2]$. It equals $\sigma^2[\Theta(1)^2+\Theta(-1)^2]/2$.