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Identification Schemes

Identification schemes for structural VAR analysis.

Cholesky

Bases: ImpulsoModel

Cholesky identification scheme.

Uses the lower-triangular Cholesky decomposition of the residual covariance matrix to identify structural shocks. Variable ordering determines the causal ordering.

Attributes:

Name Type Description
ordering list[str]

Ordered list of variable names (most exogenous first).

identify(L, var_names, posterior=None)

Apply Cholesky identification.

For default variable ordering, identify is a no-op and returns L unchanged. When self.ordering differs from var_names, the underlying covariance is permuted and re-decomposed so the Cholesky factor reflects the requested causal ordering.

Parameters:

Name Type Description Default
L ndarray

Lower-triangular Cholesky factor, shape (chains, draws, n_vars, n_vars).

 required
var_names list[str]

Variable names in the data's natural order.

 required
posterior Dataset | None

Unused. Accepted for Protocol uniformity.

 None

Returns:

Type Description
ndarray

Structural shock matrix, shape (chains, draws, n_vars, n_vars).

shock_coords(n_vars)

Cholesky shock labels are simply the causal ordering.

SignRestriction

Bases: ImpulsoModel

Sign restriction identification scheme.

Uses random rotation matrices to find structural impact matrices satisfying sign restrictions on impulse responses.

Attributes:

Name Type Description
restrictions dict[str, dict[str, str]]

Dict mapping variable -> {shock_name: "+" or "-"}.
n_rotations int

Number of candidate rotations per draw.
random_seed int | None

Seed for reproducibility.

identify(L, var_names, posterior=None)

Apply sign-restriction identification.

Parameters:

Name Type Description Default
L ndarray

Lower-triangular Cholesky factor, shape (chains, draws, n_vars, n_vars).

 required
var_names list[str]

Variable names in the data's natural order.

 required
posterior Dataset | None

Required when self.restriction_horizon > 0 because the multi-horizon check needs the VAR coefficients B from the posterior. Ignored for impact-only restrictions (restriction_horizon == 0).

 None

Returns:

Type Description
ndarray

Structural shock matrix, shape (chains, draws, n_vars, n_vars).
ndarray

Per-draw fallback to the supplied L for draws where no
ndarray

rotation satisfies the restrictions. Acceptance rate available
ndarray

via the sign_restriction_acceptance_rate attribute on the
ndarray

wrapping IdentifiedVAR's posterior (set by the pipeline).

shock_coords(n_vars)

Sign-restriction shock labels: named shocks first, then padding.