# Fourth-order moment condition for the vector GARCH equation

### Description

This function computes the fourth-order moment condition for the vector GARCH equation in the (E)CCC-GARCH models.

### Usage

1 | ```
fourth(A, B, R)
``` |

### Arguments

`A` |
an ARCH parameter matrix |

`B` |
a GARCH parameter matrix |

`R` |
a constant conditional correlation matrix |

### Value

a scalar. If strictly less than unity, the condition is satisfied.

### References

He, C. and T. Ter\"asvirta (2004):
“An Extended Constant Conditional Correlation GARCH model and its Fourth-moment Structure”,
*Econometric Theory*, **20**, 904–926.

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.

### See Also

`stationarity`