Consider the GDFM with one factor and two lags, \(\boldsymbol{z}_{t}=\boldsymbol{P}_{0} f_{t}+\boldsymbol{P}_{1} f_{t-1}+\boldsymbol{P}_{2} f_{t-3}+\boldsymbol{n}_{t}\), where the factor follows \(f_{t}=\phi f_{t-1}+u_{t}\). Prove that this model can be written as a DFM with one factor, \(\boldsymbol{z}_{t}=\boldsymbol{P}^{*} f_{t}^{*}+\boldsymbol{n}_{t}^{*}\) with \(f_{t}^{*}=\phi f_{t-1}^{*}+u_{t}^{*}\).