ARMAFIGARCHResult.persistence

property ARMAFIGARCHResult.persistence: float

Unity, by construction.

A fractionally integrated variance is not covariance stationary for any d > 0: shocks decay hyperbolically rather than geometrically, so no geometric rate describes them, and the ARCH(\(\infty\)) weights sum to \(\lambda(1) = 1\) exactly. Reporting the finite-order formula phi + beta here would produce a plausible number that means nothing, which is why GARCHResult and this class do not share one.

Example

>>> rng = np.random.default_rng(0)
>>> FIGARCH(rng.standard_normal(600)).fit().persistence
1.0