Show that the process in equation (5.110), (x_{t}=-sum_{j=0}^{infty} phi_{1}^{-j} w_{t+j}) where (left|phi_{1} ight| <1), is stationary. Note

Show that the process in equation (5.110), \(x_{t}=-\sum_{j=0}^{\infty} \phi_{1}^{-j} w_{t+j}\) where \(\left|\phi_{1}\right|<1\), is stationary.

Note an important property: in this representation \(x_{t}\) depends on future values of the white noise. (It is non-causal.)

\(x_t=-\sum_{j=0}^{\infty} \phi_1^{-j} w_{t+j} \tag{5.110}\)