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

 1  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

Note

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

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.

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