QVARResult.stability_profile#

QVARResult.stability_profile()[source]#

Largest companion-root modulus of each level’s system, ascending in tau.

Tail systems are routinely more persistent than the median system – that asymmetry is often the finding – and a modulus at or above one in a tail flags a level whose propagation reads explosively.

Return type:

NDArray[double]

Returns:

An array of length Q, aligned with quantiles.

Example

>>> import numpy as np
>>> rng = np.random.default_rng(0)
>>> y = np.zeros((300, 2))
>>> for t in range(1, 300):
...     y[t] = 0.5 * y[t - 1] + rng.standard_normal(2)
>>> res = QVAR(y, order=1).fit(quantiles=(0.1, 0.5, 0.9))
>>> roots = res.stability_profile()
>>> roots.shape, bool(np.all(roots < 1.0)), bool(np.all(np.abs(roots - 0.5) < 0.2))
((3,), True, True)
>>> QVAR(y, order=0).fit(quantiles=(0.5,)).stability_profile()
array([0.])