In the context of the exact dynamic common factor model, canonical correlations in a multivariate time series are used to identify the number of latent common factors. In this paper, we establish a relationship between canonical correlations and the autocovariance function of the factor process, in order to modify a pre-established statistical test to detect the number of common factors. In particular, the test power is increased. Additionally, we propose a procedure to identify a vector ARMA model for the factor process, which is based on the so-called simple and partial canonical autocorrelation functions. We illustrate the proposed methodology by means of some simulated examples and a real data application.