Suppose the DFM \(z_{t}=\boldsymbol{P} \boldsymbol{f}_{t}+\boldsymbol{n}_{t}\), where \(\boldsymbol{n}_{t}\) follows a diagonal VAR model. Under what conditions are the factors \(f_{t}\) linear combinations of the data? What should be the relationship between the variance of the factors and those of the noises so that we can obtain by PCA consistent estimates of the factors?