VECMXResult.generalized_irf#

VECMXResult.generalized_irf(horizon=20, *, cumulative=False)[source]#

Pesaran-Shin impulse responses, which do not depend on variable order.

The orthogonalized response asks what happens if shock j moves and the shocks ordered after it are held at zero. That question needs an order, and irf() takes it from names. The generalized response asks a different question – what happens if shock j moves and the others take their conditional expectations given that move – which needs no order at all, only the covariance.

The two agree exactly for whichever variable is placed first, and disagree for every other. Neither is more correct in general: the orthogonalized one answers a structural question and requires a defensible recursive ordering, the generalized one answers a predictive question and requires none. Reach for this when no ordering is defensible, which is the usual situation once a system spans more variables than anyone has a theory about.

Parameters:

  • horizon (int) – Periods to propagate.

  • cumulative (bool) – Accumulate the responses over the horizon.

Return type:

NDArray[double]

Returns:

An (horizon + 1, k, k) array whose [h, i, j] entry is the response of variable i at horizon h to a one-standard- deviation shock to variable j.