APARCH moment of the innovation distribution — gs_aparch

Computes $\kappa = E(|z| - \gamma z)^\delta$ for standardized innovations $z$, the quantity that enters the APARCH stationarity condition and the multi step scale forecast. A closed form is used when the distribution provides one, otherwise numerical integration.

Usage

gs_aparch_moment(dist, par, gamma, delta)

Arguments

dist: A gs_dist object.
par: Distribution parameters, named by dist$par_names.
gamma: Asymmetry parameter in (-1, 1).
delta: Power, positive.

Value

$\kappa$, or Inf when $\delta$ is not below dist$max_power(par).

References

Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83-106.

Mittnik, S., Paolella, M. S. and Rachev, S. T. (2002). Stationarity of stable power-GARCH processes. Journal of Econometrics, 106, 97-107.

Examples

gs_aparch_moment(gs_stable(), c(stable_alpha = 1.7, stable_beta = 0),
                 gamma = 0.3, delta = 1)
#> [1] 1.370884