skfolio.prior.TimeSeriesFactorModel#

class skfolio.prior.TimeSeriesFactorModel(loading_matrix_estimator=None, factor_prior_estimator=None, residual_variance=True, higham=False, max_iteration=100)[source]#

Time-series factor model estimator.

The purpose of factor models is to impose a structure on financial variables and their covariance matrix by explaining them through a small number of common factors. This reduces the number of free parameters in the estimation problem, making portfolio optimization more robust against noise. Factor models also provide a decomposition of risk into systematic and idiosyncratic components.

This estimator implements a time-series regression approach: for each asset $i$, the return is regressed on a common set of factor return series:

\[r_i(t) = \alpha_i + B_i \, f(t) + \epsilon_i(t)\]

where $B_i$ is the factor loadings (exposures), $f(t)$ is the vector of factor returns, $\alpha_i$ is the intercept, and $\epsilon_i(t)$ is the idiosyncratic return (residual).

The expected return vector is:

\[\mu = B \, \mathbb{E}[f] + \alpha\]

and the covariance matrix is:

\[\Sigma = B \, F \, B^\top + D\]

where $F$ is the factor covariance matrix and $D$ is the diagonal matrix of idiosyncratic variances.

Note

This formulation assumes that the factors are tradable assets or portfolios (e.g. long-short equity factors or ETF returns), so that the factor sample mean is a valid estimate of the factor risk premium. When factors are non-tradable variables (e.g. macroeconomic series), sometimes called a macroeconomic factor model in the literature, the sample mean no longer equals the risk premium and a two-pass procedure such as Fama-MacBeth (1973) is required to estimate the cross-sectional price of risk $\lambda$. That procedure also requires a large estimation universe in order to reliably identify the factor risk premia.

Parameters:

loading_matrix_estimatorLoadingMatrixEstimator, optional: Estimator of the loading matrix (betas) of the factors. The default (None) is to use LoadingMatrixRegression which fits the factors using LassoCV on each asset separately.
factor_prior_estimatorBasePrior, optional: Estimator of the factor return distribution. It is used to estimate the ReturnDistribution containing the factor expected returns and covariance matrix. The default (None) is to use EmpiricalPrior.
residual_variancebool, default=True: Deprecated since version The: residual_variance parameter is deprecated and will be removed in a future version. Residual variance is always added.

If this is set to True, the diagonal term of the residuals covariance (residuals variance) is added to the factor model covariance.
highambool, default=False: If this is set to True, the Higham (2002) algorithm is used to find the nearest positive semi-definite covariance matrix. It is more accurate but slower than the default clipping method. For more information see cov_nearest.
max_iterationint, default=100: Only used when higham is set to True. Maximum number of iterations of the Higham (2002) algorithm.

Attributes:

return_distribution_ReturnDistribution: Fitted ReturnDistribution containing the asset distribution and moments estimation based on the factor model.
factor_prior_estimator_BasePrior: Fitted factor_prior_estimator.
loading_matrix_estimator_BaseLoadingMatrix: Fitted loading_matrix_estimator.
n_features_in_int: Number of assets seen during fit.
feature_names_in_ndarray of shape (n_features_in_,): Names of features seen during fit. Defined only when X has feature names that are all strings.

Methods

`fit`(X, y[, factors])	Fit the Time-series factor model estimator.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`set_fit_request`(*[, factors])	Configure whether metadata should be requested to be passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.

fit(X, y, factors=None, **fit_params)[source]#

Fit the Time-series factor model estimator.

Parameters:

Xarray-like of shape (n_observations, n_assets): Price returns of the assets.
yarray-like of shape (n_observations, n_factors): Factors’ returns.
factorsarray-like of shape (n_observations, n_factors), optional: Factors’ returns. If provided, it will override y.
**fit_paramsdict: Parameters to pass to the underlying estimators. Only available if enable_metadata_routing=True, which can be set by using sklearn.set_config(enable_metadata_routing=True). See Metadata Routing User Guide for more details.

Returns:

selfTimeSeriesFactorModel: Fitted estimator.

get_metadata_routing()[source]#

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_fit_request(*, factors='$UNCHANGED$')#

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Parameters:

factorsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for factors parameter in fit.

Returns:

selfobject: The updated object.

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.