Specify an ARMA-GARCH/APARCH model — gs

The model, in the intercept form of Wuertz et al. (2006) and fGarch, is $$x_t = \mu + \sum_{i=1}^m a_i x_{t-i} + \sum_{j=1}^n b_j e_{t-j} + e_t, \qquad e_t = \sigma_t z_t,$$ $$\sigma_t^\delta = \omega + \sum_{i=1}^p \alpha_i (|e_{t-i}| - \gamma_i e_{t-i})^\delta + \sum_{j=1}^q \beta_j \sigma_{t-j}^\delta,$$ with $z_t$ i.i.d. from dist. In GARCH mode (aparch = FALSE) the asymmetry $\gamma_i$ is 0 and $\delta$ is fixed at dist$default_delta (1 for stable, 2 otherwise). mu is an intercept: the unconditional location is $\mu / (1 - \sum a_i)$. Since the innovations are location scale (not standardized), $\sigma_t$ is a conditional scale.

Usage

gs_spec(
  arma = c(0, 0),
  garch = c(1, 1),
  aparch = FALSE,
  include_mean = TRUE,
  dist = gs_stable()
)

Arguments

arma: Integer vector c(m, n), ARMA orders.
garch: Integer vector c(p, q), number of $\alpha$ (p >= 1) and $\beta$ (q >= 0) terms.
aparch: Logical, estimate the asymmetry $\gamma$ and the power $\delta$.
include_mean: Logical, include the intercept $\mu$.
dist: Innovation distribution, a gs_dist object.

Value

An object of class gs_spec.

References

Wuertz, D., Chalabi, Y. and Luksan, L. (2006). Parameter estimation of ARMA models with GARCH/APARCH errors: an R and SPlus software implementation. Journal of Statistical Software.

Examples

gs_spec(arma = c(1, 0), garch = c(1, 1), aparch = TRUE, dist = gs_stable())
#> ARMA(1,0)-APARCH(1,1) with stable innovations
#> Parameters: mu, ar1, omega, alpha1, gamma1, beta1, delta, stable_alpha, stable_beta