GARCHResult.persistence

property GARCHResult.persistence: float

The decay rate of a shock to the conditional variance.

For the level families this sums the coefficients with the asymmetry block at half weight,

\[\sum_i \alpha_i + \tfrac12 \sum_k \gamma_k + \sum_j \beta_j,\]

its unconditional frequency under a symmetric innovation distribution. For the log-variance family it is the autoregressive root of the log variance alone, \(\sum_j \beta_j\): the magnitude and sign terms are mean-zero innovations, not persistence.

Example

>>> rng = np.random.default_rng(0)
>>> y = rng.standard_normal(500)
>>> res = GARCH(y, p=1, q=1).fit()
>>> bool(np.isclose(res.persistence, res.alpha.sum() + res.beta.sum()))
True
>>> res.is_covariance_stationary
True