(a) For an \(\mathrm{AR}(2)\) model, show that \(\phi(3,3)=0\) in equation (5.129).

(b) For an \(\mathrm{AR}(2)\) model with \(\phi_{1}=\sqrt{2} ; \phi_{2}=-1 / 2\), compute the PACF. You may want to use the \(\mathrm{R}\) function ARMAacf.

\(\phi_{2,2}=\frac{\frac{\phi_1^2}{1-\phi_2}+\phi_2-\left(\frac{\phi_1}{1-\phi_2}\right)^2}{1-\left(\frac{\phi_1}{1-\phi_2}\right)^2}=\frac{ho(2)-(ho(1))^2}{1-(ho(1))^2} \tag{5.129}\)