New Test and Estimators for Common Dynamic Factors.

Federico Carlini - LUISS

Date and time
Wednesday, October 26, 2022 at 12:00 PM - In presenza + Zoom Webinar.

Contact person
Roberto RenĂ²

Publication date
September 10, 2022



We propose two new sequential testing procedures for the number q of dynamic factors in a large
dimensional dynamic factor model, and a new estimator of the dynamic factors themselves. The
testing procedures are based on two new tests for the rank of the residual covariance matrix of the
VAR model estimated on Principal Component estimators of r static factors obtained from a large
panel of observations from the dynamic factor model. The rank of the VAR residuals’ covariance
matrix is tested by deriving the asymptotically Gaussian distributions of the sum of (i) its smallest
r q eigenvalues, and (ii) the largest r  q canonical correlations between the estimated factors
and their lagged values. The canonical directions associated to the q smallest canonical correlations
allow us to define an easily implementable estimator of the common dynamic factors themselves,
and to derive its asymptotic properties. Our asymptotic results hold for relative convergence rates
of N; T more general than those required by Onatski (2009). We also introduce bootstrap versions
of our tests which perform particularly well for small values of T. Our tests provide solutions to
two unsolved problems mentioned in Bai and Ng (2007), in particular they are two examples of
tests of rank for small p.s.d. matrices, for which no theory has been developed before our paper.


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