TVPSVAR.identify

TVPSVAR.identify()

Assemble the impact path under the recursive declaration.

Return type:

TVPSVARResult

Returns:

The TVPSVARResult. For an SV source, the impact at each date is the posterior mean of A^{-1} diag(exp(h_t / 2)) across the kept draws; for a homoskedastic source it is the Cholesky factor of the posterior mean covariance, repeated.

Example

A reordered homoskedastic identification is the Cholesky factor in the new order, written back into the original positions, so it still reproduces the covariance:

>>> import numpy as np
>>> y = np.random.default_rng(0).standard_normal((120, 2))
>>> res = TVPVAR(y, order=1, training=30).fit(n_draws=12, n_burn=4, seed=0)
>>> plain = TVPSVAR(res).identify().impact(0)
>>> flipped = TVPSVAR(res, order=("y2", "y1")).identify().impact(0)
>>> bool(np.allclose(plain @ plain.T, res.sigma_u))
True
>>> bool(np.allclose(flipped @ flipped.T, res.sigma_u))
True
>>> bool(np.allclose(plain, flipped))
False
>>> bool(np.isclose(flipped[0, 1], 0.0)) or bool(np.isclose(flipped[1, 0], 0.0))
True