dlc: Various partial derivatives of the DCC part of the...

In hoanguc3m/ccgarch: Conditional Correlation GARCH models

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.

hoanguc3m/ccgarch documentation built on May 29, 2019, 11:05 p.m.