statsmodels.stats.correlation_tools.cov_nearest
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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
Parameters: cov : ndarray, (k,k)
initial covariance matrix
method : string
if ?clipped?, then the faster but less accurate
corr_clipped
is used. if ?nearest?, thencorr_nearest
is usedthreshold : float
clipping threshold for smallest eigen value, see Notes
nfact : int or float
factor to determine the maximum number of iterations in
corr_nearest
. See its doc stringreturn_all : bool
if False (default), then only the covariance matrix is returned. If True, then correlation matrix and standard deviation are additionally returned.
Returns: cov_ : ndarray
corrected covariance matrix
corr_ : ndarray, (optional)
corrected correlation matrix
std_ : ndarray, (optional)
standard deviation
See also
Notes
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.
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