GAt innovations

Generalized asymmetric t distribution of Paolella (1997) with location 0, scale 1 and parameters nu (tail), d (peakedness) and xi (asymmetry, 1 is symmetric), see dgat(). Moments \(E|z|^\delta\) exist for \(\delta < \nu d\); the GARCH mode power is \(\delta = 2\).

Usage

gs_gat(
  lower = c(nu = 0.05, d = 0.1, xi = 0.05),
  upper = c(nu = 100, d = 50, xi = 20),
  start = c(nu = 2, d = 4, xi = 1)
)

Arguments

lower, upper, start

Optional named vectors replacing the default bounds and start value.

Value

A gs_dist object.

Examples

d <- gs_gat()
d$max_power(c(nu = 2, d = 4, xi = 1))
#> [1] 8