Analytical Hessian of the (E)CCC-GARCH

Description

This function computes the analytical Hessian of the log-likelihood function of the (E)CCC-GARCH model.

Usage

1
   analytical.Hessian(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 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 npar Hessian matrix of the log-likelihood function of the (E)CCC-GARCH model

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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