Suppose that the GDFM \(z_{t}=\boldsymbol{P}_{0} f_{t}+\boldsymbol{P}_{1} f_{t-1}+\boldsymbol{a}_{t}\), where \(\boldsymbol{a}_{t}\) is white noise, is estimated by the ODPC with one lag, and \(c_{1}=c_{2}=1\). Show that the estimation of \(\boldsymbol{z}_{t}\) can be written as \(\widehat{\boldsymbol{z}}_{t}=\boldsymbol{A}_{0} \boldsymbol{z}_{t}+\boldsymbol{A}_{1} \boldsymbol{z}_{t-1}+\boldsymbol{A}_{2} \boldsymbol{z}_{t-2}\).