ccgarch (version 0.2.2)

dlc: 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 estimates of the (E)DCC parameters $(2 \times 1)$

B

the estimated GARCH parameter matrix $(N \times N)$

u

a matrix of the used for estimating the (E)DCC-GARCH model $(T \times N)$

h

a matrix of the estimated conditional variances $(T \times N)$

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.