Spillover.compute

Spillover.compute()

Read the connectedness table off the generalized decomposition.

Forms \(\Psi_h \Sigma_u e_j / \sqrt{\sigma_{jj}}\) for every lead and every shock, cumulates the squares over \(h = 0, \ldots, H\), normalizes each row to 100 and reads the directional sums off the off-diagonal.

Return type:

SpilloverResult

Returns:

The SpilloverResult, all entries in percent.

Example

The table agrees with the VAR result’s own generalized decomposition at the same horizon, and connectedness grows with the horizon as shocks propagate:

>>> import numpy as np
>>> from cultivars.multivariate.reduced_form.vector_autoregression import VAR
>>> rng = np.random.default_rng(0)
>>> y = np.zeros((300, 3))
>>> a = np.array([[0.5, 0.3, 0.0], [0.0, 0.5, 0.0], [0.0, 0.0, 0.5]])
>>> for t in range(1, 300):
...     y[t] = a @ y[t - 1] + rng.standard_normal(3)
>>> fit = VAR(y, order=1).fit()
>>> spill = Spillover(fit, horizon=10).compute()
>>> bool(np.allclose(spill.table, 100.0 * fit.generalized_fevd(10)[-1]))
True
>>> short = Spillover(fit, horizon=1).compute()
>>> bool(short.total < spill.total)
True