ccgarch (version 0.2.3)

analytical.grad: 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 in the vector GARCH equation $(N \times 1)$

A

an ARCH parameter matrix in the vector GARCH equation $(N \times N)$

B

a GARCH parameter matrix in the vector GARCH equation $(N \times N)$

R

a constant conditional correlation matrix $(N \times N)$

u

a matrix of the data used for estimating the (E)CCC-GARCH(1,1) model $(T \times N)$

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

References

Nakatani, T. and T. Ter\"asvirta (2009), “Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model”, Econometrics Journal, 12, 147--163.

Nakatani, T. and T. Ter\"asvirta (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.