I'm trying to find the autocorrelation function $\rho_x(h)$ for the Autoregressive Process $X_t = 1.2X_{t-1} - 0.5X_{t-2} + Z_t$, but I'm not sure how to derive the function.
So I know that $\rho_x(h) = \frac{\gamma_x(h)}{\gamma_x(0)}$, with $\gamma_x(h) = Cov[X_t, X_{t+h}]$, but I'm having trouble finding $Cov[X_t, X_{t+h}] = E[(1.2X_{t-1} - 0.5X_{t-2} + Z_t)(1.2X_{t+h-1} - 0.5X_{t+h-2} + Z_{t+h})]$
How do I find the autocorrelation function for this AR(2) process?