statsmodels.stats.correlation_tools.corr_clipped

statsmodels.stats.correlation_tools.corr_clipped(corr, threshold=1e-15)

Find a near correlation matrix that is positive semi-definite

This function clips the eigenvalues, replacing eigenvalues smaller than the threshold by the threshold. The new matrix is normalized, so that the diagonal elements are one. Compared to corr_nearest, the distance between the original correlation matrix and the positive definite correlation matrix is larger, however, it is much faster since it only computes eigenvalues once.

Parameters

corrndarray, (k, k)

initial correlation matrix

thresholdfloat

clipping threshold for smallest eigenvalue, see Notes

Returns

corr_newndarray, (optional)

corrected correlation matrix

See also

corr_nearest, cov_nearest

Notes

The smallest eigenvalue of the corrected correlation matrix is approximately equal to the threshold. In examples, the smallest eigenvalue can be by a factor of 10 smaller than the threshold, e.g. threshold 1e-8 can result in smallest eigenvalue in the range between 1e-9 and 1e-8. If the threshold=0, then the smallest eigenvalue of the correlation matrix might be negative, but zero within a numerical error, for example in the range of -1e-16.

Assumes input correlation matrix is symmetric. The diagonal elements of returned correlation matrix is set to ones.

If the correlation matrix is already positive semi-definite given the threshold, then the original correlation matrix is returned.

cov_clipped is 40 or more times faster than cov_nearest in simple example, but has a slightly larger approximation error.