dlc {ccgarch} | R Documentation |
This function computes various analytical derivatives of the second stage log-likelihood function (the DCC part) of the (E)DCC-GARCH model.
dlc(dcc.para, B, u, h, model)
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 |
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". |
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.