Persistence of the APARCH scale recursion — gs

Computes \(\sum_j \beta_j + \sum_i \alpha_i \kappa_i\), with \(\kappa_i = E(|z| - \gamma_i z)^\delta\) from gs_aparch_moment(). A value below 1 means \(E(\sigma_t^\delta)\) is finite (Ding, Granger and Engle, 1993; Mittnik, Paolella and Rachev, 2002). It is Inf when \(\delta\) is not below the moment bound of the innovations.

Usage

gs_stationarity(object)

Arguments

object: A gs_model or gs_fit object.

Value

The persistence, a single number.

Examples

spec <- gs_spec(garch = c(1, 1), dist = gs_stable())
m <- gs_model(spec, mu = 0, omega = 0.05, alpha = 0.1, beta = 0.8,
              dist_par = c(stable_alpha = 1.8, stable_beta = 0))
gs_stationarity(m)
#> [1] 0.9268715