Various partial derivatives of the DCC part of the log-likelihood function

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Description

This function computes various analytical derivatives of the second stage log-likelihood function (the DCC part) of the (E)DCC-GARCH model.

Usage

1
    dlc(dcc.para, B, u, h, model)

Arguments

dcc.para

the estimates of the (E)DCC parameters (2 \times 1)

B

the estimated GARCH parameter matrix (N \times N)

u

a matrix of the used for estimating the (E)DCC-GARCH model (T \times N)

h

a matrix of the estimated conditional variances (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 list with components:

dlc

the gradient of the DCC log-likelihood function w.r.t. the DCC parameters (T \times 2)

dvecP

the partial derivatives of the DCC matrix, P_t w.r.t. the DCC parameters (T \times N^{2})

dvecQ

the partial derivatives of the Q_t matrices w.r.t. the DCC parameters (T \times N^{2})

d2lc

the Hessian of the DCC log-likelihood function w.r.t. the DCC parameters (T \times 4)

dfdwd2lc

the cross derivatives of the DCC log-likelihood function (T \times npar.h+2) npar.h stand for the number of parameters in the GARCH part, npar.h = 3N for "diagonal" and npar.h = 2N^{2}+N for "extended".

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.

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