Estimation and testing of dynamic models with generalised hyperbolic innovations

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The Generalized Hyperbolic Skew Student’s t-Distribution (2006, methodology): “Further, we have χi = E(log Zi|Xi = xi) = log ( q(xi) |β| ) + 1 K ν+1 2 (|β| q(xi)) ∂K ν+1 2 (|β| q(xi)) ∂(ν+12 ) , which follows from (Mencia and Sentana, 2004) E(log Z) = ∂ E(Zr) ∂ r ∣∣∣∣ r=0 = log ( δ γ ) + 1 Kλ(δ γ) ∂ ∂ λ Kλ(δ γ).”
Multivariate GARCH Models: A Survey (2003, background): “…normal densities (see Vlaar and Palm, 1993), the Generalized Hyperbolic distribution (see Barndorff-Nielsen and Shephard (2001) for the density and Menćıa and Sentana (2003) for a recent application its standardized version in a MGARCH context) and a multivariate skew-Student density (see…”
A Multivariate Generalized Orthogonal Factor GARCH Model (2007, methodology): “Because these standard errors can be badly behaved in finite samples, as was recently pointed out by Mencía and Sentana (2004), we use their method of computing the gradient from a simulated realization of 100,000 observations.”