Suppose that $ \varepsilon_t$ is an i.i.d WN(0,1) process, that
$\alpha_t=\varepsilon_t\sqrt{1+0.35\alpha_{t-1}^2} \quad$,
$\mathcal{y{_t}}= 3+ 0.72\mathcal{y{_{t-1}}}+\alpha_t$
(a) Find the mean of $\mathcal{y{_t}}$
(b) Find the variance of $\mathcal{y{_t}}$
(c) Find the autocorrelation function of $\alpha_t^2$
I was able to get (a). Since the expectation of $\alpha_t$ is always 0 so I have: $E{[\mathcal{y{_t}}]} = \frac{3}{1-0.72}$. I'm not too sure how to proceed with (b) and (c).