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This paper studies Quasi Maximum Likelihood estimation of Dynamic FactorModels for large panels of time series. Specifically, we consider the case inwhich the autocorrelation of the factors is explicitly accounted for, andtherefore the model has a state-space form. Estimation of the factors and theirloadings is implemented through the Expectation Maximization (EM) algorithm,jointly with the Kalman smoother.~We prove that as both the dimension of thepanel $n$ and the sample size $T$ diverge to infinity, up to logarithmic terms:(i) the estimated loadings are $\sqrt T$-consistent and asymptotically normalif $\sqrt T/n\to 0$; (ii) the estimated factors are $\sqrt n$-consistent andasymptotically normal if $\sqrt n/T\to 0$; (iii) the estimated common componentis $\min(\sqrt n,\sqrt T)$-consistent and asymptotically normal regardless ofthe relative rate of divergence of $n$ and $T$. Although the model is estimatedas if the idiosyncratic terms were cross-sectionally and serially uncorrelatedand normally distributed, we show that these mis-specifications do not affectconsistency. Moreover, the estimated loadings are asymptotically as efficientas those obtained with the Principal Components estimator, while the estimatedfactors are more efficient if the idiosyncratic covariance is sparse enough.~Wethen propose robust estimators of the asymptotic covariances, which can be usedto conduct inference on the loadings and to compute confidence intervals forthe factors and common components. Finally, we study the performance of ourestimators and we compare them with the traditional Principal Componentsapproach through MonteCarlo simulations and analysis of US macroeconomic data.

Quasi Maximum Likelihood Estimation and Inference of Large Approximate Dynamic Factor Models via the EM algorithm