Expected Return Estimator

An expected return estimator estimates the expected returns (mu) of the assets.

It follows the same API as scikit-learn’s estimator: the fit method takes X as the assets returns and stores the expected returns in its mu_ attribute. X can be any array-like structure (numpy array, pandas DataFrame, etc.)

Available estimators are:

• EmpiricalMu

• EWMu

• EquilibriumMu

• ShrunkMu

For online learning and streaming workflows, EWMu supports incremental updates with partial_fit. It also supports NaN-aware updates with active_mask, which helps distinguish active assets with missing returns, for example on holidays, from structurally inactive assets such as pre-listing or post-delisting periods. See Online Learning for the full online workflow, including online portfolio optimization evaluation with incremental moments.

Example:

from skfolio.datasets import load_sp500_dataset
from skfolio.moments import EmpiricalMu
from skfolio.preprocessing import prices_to_returns

prices = load_sp500_dataset()
X = prices_to_returns(prices)

model = EmpiricalMu()
model.fit(X)
print(model.mu_)