Before revision:  The first one is based on the Hellinger distance, computed between the distribution of the eigenvalues of the empirical covariance matrix and the distribution of the eigenvalues of a reference covariance matrix . As reference distributions we use the theoretical Marchenko Pastur distribution and numerically computed ones using a random matrix of the same size as the empirical rolling matrix and constituted of Gaussian or Student-t coefficients with some simulated correlations .
After revision:  The first one is based on the Hellinger distance, computed between the distribution of the eigenvalues of the empirical covariance matrix and the distribution of the eigenvalues of a reference covariance matrix representing either a calm or agitated market .