LongRunSVAR.identify

LongRunSVAR.identify()

Factor the long-run covariance and map back to impact.

Return type:

SVARResult

Returns:

The complete structural result, shock columns ordered by permanence.

Raises:

• SpecificationError – If the autoregressive polynomial has a unit root, so no long-run impact matrix exists.

• NumericalError – If the recovered impact matrix fails to reproduce the innovation covariance, which indicates the long-run matrix is too ill-conditioned to identify through.

Example

Either ordering reproduces the innovation covariance; the long-run matrix is triangular in the declared one:

>>> import numpy as np
>>> from cultivars.multivariate.reduced_form.vector_autoregression import VAR
>>> rng = np.random.default_rng(0)
>>> y = np.zeros((402, 2))
>>> for t in range(1, 402):
...     y[t] = 0.4 * y[t - 1] + rng.standard_normal(2)
>>> res = VAR(y, order=1, names=("dy", "u")).fit()
>>> first = LongRunSVAR(res).identify()
>>> second = LongRunSVAR(res, order=("u", "dy")).identify()
>>> bool(abs(first.long_run_impact[0, 1]) < 1e-10)
True
>>> bool(abs(second.long_run_impact[1, 1]) < 1e-10), second.shock_names
(True, ('u', 'dy'))
>>> bool(np.allclose(second.impact @ second.impact.T, res.sigma_u))
True