Consider the stationary process $X_t= \rho X_{t-1} + \epsilon_t$ in which {$\epsilon_t$} is a serie of random shocks with zero mean and variance $\sigma^2_{\epsilon}$. Also, consider another serie of random shocks {$W_t$} with zero mean and variance $\sigma^2_{W}$, in a way that $E[\epsilon_t W_s] = 0 \forall s,t$. Be $Y_t = X_t + W_t$, find the autocovariance of the process $Y_t$.
—-
My work, so far was first try to prove that $Y_t$ is stationary..