SignRestrictedSVARResult.fevd#

SignRestrictedSVARResult.fevd(horizon=20, *, quantiles=(0.16, 0.5, 0.84))[source]#

Pointwise quantiles of the variance decomposition across the set.

Each accepted rotation is complete, so within a rotation the shares sum to one; the quantile surfaces, being pointwise, need not – except with two variables, where the second share is one minus the first and the quantiles mirror exactly.

Parameters:

  • horizon (int) – Largest lead to return.

  • quantiles (Sequence[float]) – Probability levels, each in (0, 1).

Return type:

NDArray[double]

Returns:

An array of shape (len(quantiles), horizon + 1, k, k); entry [q, h, i, j] is the q-quantile of shock j’s share of variable i’s forecast-error variance at lead h.

Raises:

SpecificationError – If a quantile is outside the open unit interval.

Example

>>> import numpy as np
>>> from cultivars.multivariate.reduced_form.vector_autoregression import VAR
>>> rng = np.random.default_rng(0)
>>> res = VAR(rng.standard_normal((121, 3)), order=1).fit()
>>> sset = SignRestrictedSVAR(res, {"d": {"y1": "+"}}, draws=50, seed=0).identify()
>>> shares = sset.fevd(3)
>>> shares.shape, bool(np.all((0.0 <= shares) & (shares <= 1.0)))
((3, 4, 3, 3), True)
>>> draws = sset.irf_draws(3)
>>> explained = np.cumsum(draws**2, axis=1)
>>> own = explained / explained.sum(axis=3, keepdims=True)
>>> bool(np.allclose(own.sum(axis=3), 1.0))
True
>>> bool(np.allclose(shares[1].sum(axis=2), 1.0))
False