# 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 |

`A` |
an ARCH parameter matrix in the vector GARCH equation |

`B` |
a GARCH parameter matrix in the vector GARCH equation |

`R` |
a constant conditional correlation matrix |

`u` |
a matrix of the data used for estimating the (E)CCC-GARCH(1,1) model |

`model` |
a character string describing the 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.

Want to suggest features or report bugs for rdrr.io? Use the GitHub issue tracker. Vote for new features on Trello.