Full question:
$X_0,X_1, …., X_n$ are distributed according to the following AR(2) process
$$X_i = 0.3X_{i-2} + u_i$$
for $i=1,...,n$, $X_0=X_1=0$, and $u_i$ are iid $N(0,3^2)$.
Have no idea where to start with this one.
Any help would be much appreciated.
Here is what I know:
$$E(X_i) = E(.3X_{i-2} + u_i) = .3E(X_{i-2})+E(u_i) = 3(0)+0$$
What I have tried: \begin{align*} Var(X_i)&= Var(.3X_{i-2} + u_i)\\ &=.3^2(Var(X_{i-2}))+Var(u_i)\\ &= .3^2(Var(X_{i-2}))+9\\ &= ? \end{align*}
I don't know how to take the variance of $X_{i-2}$ because when you expand it, you get a ton more $u_i$s that I don't know what to do with
[self-study]
tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$