Correlation Matrix Distance

Compute the distance between an asset correlation matrix and a reference correlation matrix, using one of the following distance metrics:

• Euclidean distance (default), which is the distance induced by the Frobenius norm
• Correlation matrix distance, defined in the first reference, which corresponds to the cosine distance between the two vectorized asset correlation matrices
• Bures distance, defined in the second reference

References

• M. Herdin, N. Czink, H. Ozcelik and E. Bonek, Correlation matrix distance, a meaningful measure for evaluation of non-stationary MIMO channels, 2005 IEEE 61st Vehicular Technology Conference, 2005, pp. 136-140 Vol. 1
• Rajendra Bhatia, Tanvi Jain, Yongdo Lim, On the Bures–Wasserstein distance between positive definite matrices, Expositiones Mathematicae, Volume 37, Issue 2, 2019