How can I generate two correlated $AR(1)$ data series with given correlation between $d_{1,t}$ and $d_{2,t}$, $r_{12}$, where $\rho_{12}$ is correlation between the two error series $$d_{1,t}=\mu+\phi_1d_{1,(t−1)}+e_{1}(t)\quad\quad d_{2,t}=\mu+\phi_2d_{2,(t-1)}+e_{2}(t)$$
$e_1$ and $e_2$ are not the same and $r_{12}$ is desired correlation between $d_{1,t}$ and $d_{2,t}$. The relations between $r_{12}$ and $\rho_{12}$ is:
$$r_{12}=\rho_{12}*\sqrt{(1-\phi_1^2)*(1-\phi_2^2)}/ (1-\phi_1\phi_2)$$
one example for: $\phi_1=.3$, $\phi_2=-.8$ AND $r_{12}=-.8$; the problem is, for this example $\rho_{12}$ is $-1.7$, now how can I generate the error terms where the correlation between the two error series $\rho_{12}$ is not between $-1$ and $+1$. please help me if i'm wrong somewhere. THANKS YOU
