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

Abstract

 This paper studies Quasi Maximum Likelihood estimation of approximate Dynamic Factor Models for large panels of time series. Specifically, we consider the case in which the autocorrelation of the factors is explicitly accounted for and therefore the model has a state-space form. Estimation of the factors and of their loadings is implemented by means of the Expectation Maximization (EM) algorithm, jointly with the Kalman smoother. We prove that, as both the dimension of the panel  and the sample size  diverge to infinity: (i) the estimated loadings are -consistent and asymptotically normal if ; (ii) the estimated factors are -consistent and asymptotically normal  if ; (iii) the estimated common component is -consistent and asymptotically normal regardless of the relative rate of divergence of  and . Although the model is estimated as if the  idiosyncratic terms were cross-sectionally and serially uncorrelated, and normally distributed, we show that these mis-specifications do not affect consistency. Moreover, the estimated loadings are asymptotically as efficient as those obtained with the Principal Components estimator, while the estimated factors are more efficient if the idiosyncratic covariance is sparse enough. We then propose robust estimators of the asymptotic covariances, which can be used to conduct inference on the loadings and to compute confidence intervals for the factors and common components. Finally, we study the performance of our estimators and we compare them with the traditional Principal Components approach by means of Monte Carlo simulations and an analysis of US macroeconomic data.

 Coauthor: Matteo Luciani, Federal Reserve Board, Washington

 Keywords: Approximate Dynamic Factor Model; Expectation Maximization Algorithm; Kalman Smoother; Quasi Maximum Likelihood.

 Disclaimer: the views expressed in this paper are those of the authors and do not necessarily reflect the views and policies of the Board of Governors or the Federal Reserve System.

        L’Organizzatore                                                                                                                                  Il Direttore   

     Prof. Matteo Farnè                                                                                                                             Prof. Carlo Trivisano

La S.V. è invitata