def min_cov_determinant(prices, frequency=252, random_state=None):
"""
Calculate the minimum covariance determinant, an estimator of the covariance matrix
that is more robust to noise.
:param prices: adjusted closing prices of the asset, each row is a date
and each column is a ticker/id.
:type prices: pd.DataFrame
:param frequency: number of time periods in a year, defaults to 252 (the number
of trading days in a year)
:type frequency: int, optional
:param random_state: random seed to make results reproducible, defaults to None
:type random_state: int, optional
:return: annualised estimate of covariance matrix
:rtype: pd.DataFrame
"""
if not isinstance(prices, pd.DataFrame):
warnings.warn("prices are not in a dataframe", RuntimeWarning)
prices = pd.DataFrame(prices)
assets = prices.columns
X = prices.pct_change().dropna(how="all")
X = np.nan_to_num(X.values)
raw_cov_array = covariance.fast_mcd(X, random_state=random_state)[1]
return pd.DataFrame(raw_cov_array, index=assets,
columns=assets) * frequency
def _mcd(X):
"""Wrapper for sklearn mcd covariance estimator.
Parameters
----------
X : ndarray
EEG signal, shape (n_channels, n_samples).
Returns
-------
C : ndarray
Estimated covariance, shape (n_channels, n_channels).
"""
_, C, _, _ = fast_mcd(X.T)
return C
def launch_mcd_on_dataset(n_samples, n_features, n_outliers,
tol_loc, tol_cov, tol_support, correction):
"""
"""
data = np.random.randn(n_samples, n_features)
# add some outliers
outliers_index = np.random.permutation(n_samples)[:n_outliers]
outliers_offset = 10. * \
(np.random.randint(2, size=(n_outliers, n_features)) - 0.5)
data[outliers_index] += outliers_offset
inliers_mask = np.ones(n_samples).astype(bool)
inliers_mask[outliers_index] = False
# compute MCD directly
T, S, H = fast_mcd(data, correction=correction)
# compare with the estimates learnt from the inliers
pure_data = data[inliers_mask]
error_location = np.sum((pure_data.mean(0) - T) ** 2)
assert(error_location < tol_loc)
emp_cov = EmpiricalCovariance().fit(pure_data)
#print emp_cov.error_norm(S)
assert(emp_cov.error_norm(S) < tol_cov)
assert(np.sum(H) > tol_support)
# check improvement
if (n_outliers / float(n_samples) > 0.1) and (n_features > 1):
error_bad_location = np.sum((data.mean(0) - T) ** 2)
assert(error_bad_location > error_location)
bad_emp_cov = EmpiricalCovariance().fit(data)
assert(emp_cov.error_norm(S) < bad_emp_cov.error_norm(S))
# compute MCD by fitting an object
mcd_fit = MCD().fit(data)
T = mcd_fit.location_
S = mcd_fit.covariance_
H = mcd_fit.support_
# compare with the estimates learnt from the inliers
error_location = np.sum((pure_data.mean(0) - T) ** 2)
assert(error_location < tol_loc)
assert(emp_cov.error_norm(S) < tol_cov)
assert(np.sum(H) > tol_support)
# check improvement
if (n_outliers / float(n_samples) > 0.1) and (n_features > 1):
error_bad_location = np.sum((data.mean(0) - T) ** 2)
assert(error_bad_location > error_location)
bad_emp_cov = EmpiricalCovariance().fit(data)
assert(emp_cov.error_norm(S) < bad_emp_cov.error_norm(S))
def min_cov_determinant(prices, frequency=252, random_state=None):
"""
Calculate the minimum covariance determinant, an estimator of the covariance matrix
that is more robust to noise.
:param prices: adjusted closing prices of the asset, each row is a date
and each column is a ticker/id.
:type prices: pd.DataFrame
:param frequency: number of time periods in a year, defaults to 252 (the number
of trading days in a year)
:type frequency: int, optional
:param random_state: random seed to make results reproducible, defaults to None
:type random_state: int, optional
:return: annualised estimate of covariance matrix
:rtype: pd.DataFrame
"""
if not isinstance(prices, pd.DataFrame):
warnings.warn("prices are not in a dataframe", RuntimeWarning)
prices = pd.DataFrame(prices)
assets = prices.columns
X = prices.pct_change().dropna(how="all")
X = np.nan_to_num(X.values)
raw_cov_array = covariance.fast_mcd(X, random_state=random_state)[1]
return pd.DataFrame(raw_cov_array, index=assets, columns=assets) * frequency
def _mcd(X):
"""Wrapper for sklearn mcd covariance estimator"""
_, C, _, _ = fast_mcd(X.T)
return C
def _mcd(X):
"""Wrapper for sklearn mcd covariance estimator"""
_, C, _, _ = fast_mcd(X.T)
return C
def test_fast_mcd_on_invalid_input():
X = np.arange(100)
msg = "Expected 2D array, got 1D array instead"
with pytest.raises(ValueError, match=msg):
fast_mcd(X)
