The log-likelihood and its analytic gradient with respect to
(μ, ω, α, γ, β) — and ν, a sixth entry, for t and skewed-t innovations, λ
a seventh for skewed t; with an exogenous x, δ is the eighth (ν's and λ's
entries 0 where they are absent). With scores, also each observation's
gradient — a row of n per parameter, in the same order — for the robust
covariance.
The log-likelihood and its analytic gradient with respect to (μ, ω, α, γ, β) — and ν, a sixth entry, for t and skewed-t innovations, λ a seventh for skewed t; with an exogenous x, δ is the eighth (ν's and λ's entries 0 where they are absent). With
scores, also each observation's gradient — a row of n per parameter, in the same order — for the robust covariance.