analytical.grad {ccgarch}R Documentation

Analytical gradient of the log-likelihood function of the (E)CCC-GARCH(1,1) model

Description

This function returns the analytical gradient of the log-likelihood function of the (E)CCC-GARCH(1,1) model.

Usage

   analytical.grad(a, A, B, R, u, model)

Arguments

a a vector of constants (N times 1)
A an ARCH parameter matrix (N times N)
B a GARCH parameter matrix (N times N)
R a constant conditional correlation (N times N)
u a matrix of the observed residuals (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 (npar times T) matrix of gradients

Note

In the output, each column (not row) corresponds to the gradient at observation t.

References

Nakatani, T. and T. er"{a}svirta (2008), “Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model”, Econometrics Journal, forthcoming.

Nakatani, T. and T. Ter"{a}svirta (2008), “Appendix to Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model” Department of Economic Statistics, Stockholm School of Economics, available at http://swopec.hhs.se/hastef/abs/hastef0649.htm.


[Package ccgarch version 0.1.1 Index]