logLikDccGarch {bayesDccGarch}

The logarithm of likelihood function of DCC-GARCH(1,1) Model.

Description

Compute the logarithm of likelihood function of DCC-GARCH(1,1) Model if mY is a matrix or the logarithm of likelihood function of GARCH(1,1) Model if mY is numeric vector.

Usage

logLikDccGarch(mY, omega = rep(0.03, ncol(mY)), alpha = rep(0.03, ncol(mY)), 
	beta = rep(0.8, ncol(mY)), a = 0.03, b = 0.8, gamma = rep(1, ncol(mY)), 
	tail = 10, errorDist = 2)

Arguments

mY

a matrix of the data (n \times k).

omega

a numeric vector (k \times 1) with the the values of \omega_i parameters. Default: rep(0.03, ncol(mY)).

alpha

a numeric vector (k \times 1) with the the values of \alpha_i parameters. Default: rep(0.03, ncol(mY)).

beta

a numeric vector (k \times 1) with the the values of \beta_i parameters. Default: rep(0.80, ncol(mY)).

a

a numeric value of the a parameter. Default: 0.03.

b

a numeric value of the b parameter. Default: 0.8.

gamma

a numeric vector (k \times 1) with the values of \gamma_i parameters. Default: rep(1.0, ncol(mY)).

tail

a numeric value of \nu parameter if errorDist = 2 or of \delta parameter if errorDist = 3. If errorDist = 1 so this arguments is no used.

errorDist

a probability distribution for errors. Use errorDist=1 for SSNorm, errorDist=2 for SST or errorDist=3 for SSGED. Default: 2.

Details

The log-likelihood of the model GARCH(1,1) is computed if mY has just one column. The arguments a and b are not consider in this case.

Value

Return a list with the elements:

$H

a matrix where the lines are the H_t values for t=1,...,n.

$value

the value of the logarithm of likelihood function.

Author(s)

Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada

References

Fioruci, J.A., Ehlers, R.S., Andrade Filho, M.G. Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions, Journal of Applied Statistics, 41(2), 320–331, 2014a. <doi:10.1080/02664763.2013.839635>

Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. https://ui.adsabs.harvard.edu/abs/2014arXiv1412.2967F/abstract.

See Also

bayesDccGarch-package, bayesDccGarch

Examples

data(DaxCacNik)

Dax = DaxCacNik[,1]

######  log-likelihood function of GARCH(1,1) model with SST innovations ####
logLikDccGarch(Dax, omega=0.03, alpha=0.03, beta=0.8, gamma=0.7)$value

######  log-likelihood function of DCC-GARCH(1,1) model with SST innovations ####
logLikDccGarch(DaxCacNik, beta=c(0.82,0.91,0.85), gamma=c(0.7, 1.3, 1.7), tail=10)$value