ccgarch (version 0.2.3)

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 Statistics 20, 339--350.

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

See Also

dcc.estimation