Let an autoregressive sequence of order (2left{Y_{t} ; t=0, pm 1, pm 2, ldots ight}) be given

Let an autoregressive sequence of order \(2\left\{Y_{t} ; t=0, \pm 1, \pm 2, \ldots\right\}\) be given by

\[Y_{t}-1.6 Y_{t-1}+0.68 Y_{t-2}=2 X_{t} ; \quad t=0, \pm 1, \pm 2, \ldots\]

where \(\left\{X_{t} ; t=0, \pm 1, \pm 2, \ldots\right\}\) is the same purely random sequence as in the previous exercise.

(1) Is the the sequence \(\left\{Y_{t} ; t=0, \pm 1, \pm 2, \ldots\right\}\) weakly stationary?

(2) Determine its covariance and correlation function.