Eigenvalue Ratio Estimators for the Number of Dynamic Factors

In this paper we introduce three dynamic eigenvalue ratio estimators for the number of
dynamic factors. Two of them, the Dynamic Eigenvalue Ratio (DER) and the Dynamic Growth Ratio
(DGR) are dynamic counterparts of the eigenvalue ratio estimators (ER and GR) proposed by Ahn
and Horenstein (2013). The third, the Dynamic eigenvalue Difference Ratio (DDR), is a new one but
closely related to the test statistic proposed by Onatsky (2009). The advantage of such estimators is that
they do not require preliminary determination of discretionary parameters. Finally, a static counterpart
of the latter estimator, called eigenvalue Difference Ratio estimator (DR), is also proposed. We prove
consistency of such estimators and evaluate their performance under simulation. We conclude that both
DDR and DR are valid alternatives to existing criteria. Application to real data gives new insights on
the number of factors driving the US economy.