I've got the following problem. I have two AR(1) processes (which are the returns on assets)-
$r_{1t} = \phi_1r_{1,t-1} + u_{1t},$ $r_{2t} = \phi_2r_{2,t-1} + u_{2t},$
We have the following weighted portfolio of these two returns as:
$rp_t = \frac{r_{1t} + r_{2t}}{2}$
And we must represent $rp_t$ as an ARMA. Obviously I have subbed in the original definitions and got
$rp_t = \frac{\phi_1r_{1,t-1} + \phi_2r_{2,t-2}}{2} + \frac{u_{1t} + u_{2t}}{2}$
but I guess I really need to express $rp_t$ in terms of $rp_{t-1}$ or previous terms plus some error terms - i.e. how do I get rid of the $\phi_1$ and $\phi_2$ in the expansion immediately above?
Any help greatly appreciated as I've been struggling with this for ages, and I will be sure to vote up any helpful answers.
Apologies if this question is a duplicate, but I can't seem to find it already.
PW