Fourth-order moment condition for the vector GARCH equation

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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 (N \times N)

B

a GARCH parameter matrix (N \times N)

R

a constant conditional correlation matrix (N \times N)

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

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