dlv {ccgarch}R Documentation

Gradient of the GARCH part of the log-likelihood function of the 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 observed residuals (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


[Package ccgarch version 0.1.1 Index]