GVARResult.sigma_ml

property GVARResult.sigma_ml: NDArray[float64]

Innovation covariance without the degrees-of-freedom correction.

Example

>>> import numpy as np
>>> from cultivars.multivariate.reduced_form.vector_autoregression import VARX
>>> y = np.random.default_rng(0).standard_normal((200, 2))
>>> units = [VARX(y[:, [i]], y[:, [1 - i]], order=1).fit() for i in (0, 1)]
>>> swap = np.array([[0.0, 1.0], [1.0, 0.0]])
>>> names = ("us", "eu")
>>> res = GVAR(units, swap, variable_labels=["p", "p"], unit_names=names).solve()
>>> bool(np.allclose(res.sigma_ml * res.nobs, res.resid.T @ res.resid))
True
>>> bool(np.all(np.diag(res.sigma_ml) < np.diag(res.sigma_u)))
True