dlv: Gradient of the GARCH part of the log-likelihood function of an (E)DCC-GARCH model
Description
This function returns the analytical partial derivatives of the volatility part of
the log-likelihood function of the DCC-GARCH model.
The function is called from dcc.results.
Usage
dlv(u, a, A, B, model)
Arguments
u
a matrix of the data used for estimating an (E)DCC-GARCH model $(T \times N)$
a
a vector of the constants in the volatility part $(N \times 1)$
A
an ARCH parameter matrix $(N \times N)$
B
a GARCH parameter matrix $(N \times N)$
model
a character string describing the model."diagonal" for the diagonal model
and "extended" for the extended (full ARCH and GARCH parameter matrices) model
Value
A matrix of partial derivatives. $(T \times npar.h)$ where $npar.h$ stand for
the number of parameters in the GARCH part, $npar.h = 3N$ for "diagonal" and
$npar.h = 2N^{2}+N$ for "extended".
References
Engle, R.F. and K. Sheppard (2001),
Theoretical and Empirical Properties of Dynamic
Conditional Correlation Multivariate GARCH.Stern Finance Working Paper Series
FIN-01-027 (Revised in Dec. 2001),
New York University Stern School of Business.
Engle, R.F. (2002),
Dynamic Conditional Correlation: A Simple Class of
Multivariate Generalized Autoregressive Conditional
Heteroskedasticity Models.Journal of Business and Economic Statistics20, 339--350.
Hafner, C.M. and H. Herwartz (2008),
Analytical Quasi Maximum Likelihood Inference in Multivariate Volatility Models.Metrika67, 219--239.