dlc {ccgarch}R Documentation

Various partial derivatives of the DCC part of the log-likelihood function

Description

This function computes various analytical derivatives of the second stage log-likelihood function (the DCC part) of the (E)DCC-GARCH model.

Usage


    dlc(dcc.para, B, u, h, model)

Arguments

dcc.para the estimated DCC parameters (2 times 1)
B the estimated GARCH matrix (N times N)
u a matrix of the observed residuals (T times N)
h a matrix of the estimated volatilities (T 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 list with components:

dlc the gradient of the DCC log-likelihood function w.r.t. the DCC parameters (T times 2)
dvecP the partial derivatives of the DCC matrix, P_t w.r.t. the DCC parameters (T times N^{2})
dvecQ the partial derivatives of the Q_t matrices w.r.t. the DCC parameters (T times N^{2})
d2lc the Hessian of the DCC log-likelihood function w.r.t. the DCC parameters (T times 4)
dfdwd2lc the cross derivatives of the DCC log-likelihood function (T times npar.h+2) 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 Statistics 20, 339-350.

Hafner, C.M. and H. Herwartz (2008), “Analytical Quasi Maximum Likelihood Inference in Multivariate Volatility Models” Metrika 67, 219–239.


[Package ccgarch version 0.1.1 Index]