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# skfolio.utils.stats.cov_nearest

<a id="skfolio.utils.stats.cov_nearest"></a>

### skfolio.utils.stats.cov_nearest(cov, higham=False, higham_max_iteration=100, warn=False)

Compute the nearest covariance matrix that is positive definite and with a
cholesky decomposition that can be computed. The variance is left unchanged.
A covariance matrix that is not positive definite often occurs in high
dimensional problems. It can be due to multicollinearity, floating-point
inaccuracies, or when the number of observations is smaller than the number of
assets.

First, it converts the covariance matrix to a correlation matrix.
Then, it finds the nearest correlation matrix and converts it back to a covariance
matrix using the initial standard deviation.

Cholesky decomposition can fail for symmetric positive definite (SPD) matrix due
to floating point error and inversely, Cholesky decomposition can succeed for
non-SPD matrix. Therefore, we need to test for both. We always start by testing
for Cholesky decomposition which is significantly faster than checking for positive
eigenvalues.

* **Parameters:**
  **cov** *ndarray of shape (n, n)*
  : Covariance matrix.

  **higham** *bool, default=False*
  : If this is set to True, the Higham (2002) algorithm [[1]](#r06f528358d09-1) is used,
    otherwise the eigenvalues are clipped to threshold above zeros (1e-13).
    The default (`False`) is to use the clipping method as the Higham
    algorithm can be slow for large datasets.

  **higham_max_iteration** *int, default=100*
  : Maximum number of iterations of the Higham (2002) algorithm.
    The default value is `100`.

  **warn** *bool, default=False*
  : If this is set to True, a user warning is emitted when the covariance matrix
    is not positive definite and replaced by the nearest. The default is False.
* **Returns:**
  **cov** *ndarray*
  : The nearest covariance matrix.

### References

* <a id='r06f528358d09-1'>**[1]**</a> “Computing the nearest correlation matrix - a problem from finance” IMA Journal of Numerical Analysis Higham (2002)