skfolio.moments.GerberCovariance#

class skfolio.moments.GerberCovariance(window_size=None, threshold=0.5, psd_variant=True, nearest=True, higham=False, higham_max_iteration=100)[source]#

Gerber Covariance estimator.

Robust co-movement measure which ignores fluctuations below a certain threshold while simultaneously limiting the effects of extreme movements. The Gerber statistic extends Kendall’s Tau by counting the proportion of simultaneous co-movements in series when their amplitudes exceed data-dependent thresholds.

Three variant has been published:

  • Gerber et al. (2015): tend to produce matrices that are non-PSD.

  • Gerber et al. (2019): alteration of the denominator of the above statistic.

  • Gerber et al. (2022): final alteration to ensure PSD matrix.

The last two variants are implemented.

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.

thresholdfloat, default=0.5

Gerber threshold. The default value is 0.5.

psd_variantbool, default=True

If this is set to True, the Gerber et al. (2022) variant is used to ensure a positive semi-definite matrix. Otherwise, the Gerber et al. (2019) variant is used. The default is True.

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.

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.

References

[1]

“The gerber statistic: A robust co-movement measure for portfolio optimization”. The Journal of Portfolio Management. Gerber, S., B. Javid, H. Markowitz, P. Sargen, and D. Starer (2022).

[2]

“The gerber statistic: A robust measure of correlation”. Gerber, S., B. Javid, H. Markowitz, P. Sargen, and D. Starer (2019).

[3]

“Enhancing multi-asset portfolio construction under modern portfolio theory with a robust co-movement measure”. Social Science Research network Working Paper Series. Gerber, S., H. Markowitz, and P. Pujara (2015).

[4]

“Deconstructing the Gerber Statistic”. Flint & Polakow, 2023.

Methods

fit(X[, y])

Fit the Gerber 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)[source]#

Fit the Gerber 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:
selfGerberCovariance

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.