This function returns the negative of the log-Likelihood function for GO-GARCH models.
gollh(params, object, garchlist)Vector of initial values for theta.
An object of class Goinit or an extension thereof.
List, elements are passed to garchFit.
Scalar, the negative value of the log-Likelihood function.
The log-Likelihood function of GO-GARCH models is given as:
$$ L_{\theta, \alpha, \beta} = - \frac{1}{2} \sum_{t=1}^T m \log(2\pi) + \log|Z_\theta Z_\theta '| + \log|H_t| + y' H_t^{-1}y_t $$ whereby \(Z = P \Delta^{\frac{1}{2}} U_0\), \(y_t = Z^{-1}x_t\) and \(H_t\) is the conditional variance matrix of the independent components.
Van der Weide, Roy (2002), GO-GARCH: A Multivariate Generalized Orthogonal GARCH Model, Journal of Applied Econometrics, 17(5), 549 -- 564.