statsmodels.stats.correlation_tools.cov_nearest(cov, method='clipped', threshold=1e-15, n_fact=100, return_all=False)[source]

Find the nearest covariance matrix that is postive (semi-) definite

This leaves the diagonal, i.e. the variance, unchanged

  • cov (ndarray, (k,k)) – initial covariance matrix

  • method (string) – if “clipped”, then the faster but less accurate corr_clipped is used.if “nearest”, then corr_nearest is used

  • threshold (float) – clipping threshold for smallest eigen value, see Notes

  • n_fact (int or float) – factor to determine the maximum number of iterations in corr_nearest. See its doc string

  • return_all (bool) – if False (default), then only the covariance matrix is returned. If True, then correlation matrix and standard deviation are additionally returned.


  • cov_ (ndarray) – corrected covariance matrix

  • corr_ (ndarray, (optional)) – corrected correlation matrix

  • std_ (ndarray, (optional)) – standard deviation


This converts the covariance matrix to a correlation matrix. Then, finds the nearest correlation matrix that is positive semidefinite and converts it back to a covariance matrix using the initial standard deviation.

The smallest eigenvalue of the intermediate correlation matrix is approximately equal to the threshold. 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 covariance matrix is symmetric.