Gradient of the GARCH part of the log-likelihood function of an (E)DCC GARCH model

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Description

This function returns the gradient of the volatility part of the log-likelihood function of the DCC.

Usage

1
    dlv.est(par, dvar, model)

Arguments

par

a vector of the parameters in the vector GARCH equation

dvar

a matrix of the data used for estimating an (E)DCC-GARCH 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 vector of the gradient. (3N \times 1) for "diagonal" and (2N^{2}+N \times 1) for "extended".

Note

The function can be called from optim in dcc.estimation1. For obtaining the gradient for all t, use dlv instead.

References

Engle, R.F. and K. Sheppard (2001), “Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH.” Stern Finance Working Paper Series FIN-01-027 (Revised in Dec. 2001), New York University Stern School of Business.

Engle, R.F. (2002), “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Journal of Business and Economic Statistics 20, 339–350.

Hafner, C.M. and H. Herwartz (2008), “Analytical Quasi Maximum Likelihood Inference in Multivariate Volatility Models.” Metrika 67, 219–239.

See Also

dcc.estimation1, dlv

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