This function returns the negative of the log-Likelihood function for
GO-GARCH models.
Usage
gollh(params, object, garchlist)
Arguments
params
Vector of initial values for theta.
object
An object of class Goinit or an extension thereof.
garchlist
List, elements are passed to garchFit.
Value
negllScalar, the negative value of the log-Likelihood function.
encoding
latin1
concept
GO-GARCH
Likelihood
Details
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.
References
Van der Weide, Roy (2002), GO-GARCH: A Multivariate Generalized
Orthogonal GARCH Model, Journal of Applied Econometrics,
17(5), 549 -- 564.