Comments and Questions

I think the paper makes an important contribution in clarifying the numerical implications of the theoretical contribution by Doz et al (2012). It is a very nice and clear exposition of the estimation techniques for dynamic factor models and their pros and cons. I have the following minor comments 1. After eq (2) the series are also centered so they have mean zero and variance one. None of the two hypothesis is restrictive. You can of course add a constant term, while you need to standardize only if variables are measured with different units. 2. In the introduction say that Doz et al (2011) is adopting solution (a) while solution (b) is in Doz et al (2012). 3. Forni et al (2005) is not really considering s to be infinite, indeed they apply some weighted PCAs in time domain. It is an hybrid approach but for the sake of simplicity I would not include it among the unrestricted gdfm papers. 4. An important difference between your dgp and Doz et al (2012) is that in eq (1) you allow for lags. It is an important contribution that you're making and I think you should stress this more in section 2. 5. A measure which is equally important to report is the MSE between the estimated common component and the simulated one. 6. The static representation of (1)-(2) is valid of course but you cannot hope to estimate the dynamic factors f once you have the static ones F. In fact what you say is that you are interested in F, not in f. But that makes sense to me only if the common component is your interest but if you want to attach a "meaning" to the factors then f should be your interest and you cannot recover them from F. For this reason I think studying the MSE of the estimated common component instead would be important since it is not affected by identification issues. 7. On page 8 step 3, why do you extract qs PC? shouldn't be q(s+1) PC? 8. There are two recent papers studying the asymptotic properties of the EM estimation of stationary factor models with singular factors (Barigozzi Luciani, 2019a) and of non-stationary dynamic factor models, where factors are loaded with lags, s>0 (Barigozzi Luciani, 2019b) please refer also to those papers and the simulation results therein. REFERENCES Barigozzi Luciani, 2019a, "Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm", arxiv:1910.03821 Barigozzi Luciani, 2019b, "Quasi Maximum Likelihood Estimation of Non-Stationary Large Approximate Dynamic Factor Models", arXiv:1910.09841