skfolio.moments.EmpiricalCovariance

class skfolio.moments.EmpiricalCovariance(window_size=None, ddof=1, nearest=True, higham=False, higham_max_iteration=100)

Empirical Covariance estimator.

Parameters:

window_sizeint, optional

Window size. The model is fitted on the last window_size observations. The default (None) is to use all the data.

ddofint, default=1

Normalization is by (n_observations - ddof). Note that ddof=1 will return the unbiased estimate, and ddof=0 will return the simple average. The default value is 1.

nearestbool, default=True

If this is set to True, the covariance is replaced by the nearest covariance matrix that is positive definite and with a Cholesky decomposition than 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. For more details, see cov_nearest. The default is True.

highambool, default=False

If this is set to True, the Higham & Nick (2002) algorithm is used to find the nearest PD covariance, otherwise the eigenvalues are clipped to a threshold above zeros (1e-13). The default is False and use the clipping method as the Higham & Nick algorithm can be slow for large datasets.

higham_max_iterationint, default=100

Maximum number of iteration of the Higham & Nick (2002) algorithm. The default value is 100.

Attributes:

covariance_ndarray of shape (n_assets, n_assets)

Estimated covariance matrix.

n_features_in_int

Number of assets seen during fit.

feature_names_in_ndarray of shape (n_features_in_,)

Names of assets seen during fit. Defined only when X has assets names that are all strings.

Methods

fit(X[, y])	Fit the empirical covariance estimator.
get_metadata_routing()	Get metadata routing of this object.
get_params([deep])	Get parameters for this estimator.
set_params(**params)	Set the parameters of this estimator.

fit(X, y=None)

Fit the empirical covariance estimator.

Parameters:

Xarray-like of shape (n_observations, n_assets)

Price returns of the assets.

yIgnored

Not used, present for API consistency by convention.

Returns:

selfEmpiricalCovariance

Fitted estimator.

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict

Parameter names mapped to their values.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.