Question $1 $ For an MA(1), $X_{t}=W_{t}+\theta W_{t-1}, W_{t} \sim W N\left(0, \sigma^{2} ight)$, show that $ ho_{x}(1) \leq 1 / 2$ for any number $\theta$. For which values of $\theta$ does $ ho_{x}(1)$ attain its maximum and minimum? SP.PC.056