bayesDccGarch {bayesDccGarch} | R Documentation |
Performs a Markov Chain for all parameters of the DCC-GARCH(1,1) Model.
bayesDccGarch(mY, nSim = 10000, tail_ini = 8, omega_ini = rep(0.03, ncol(mY)), alpha_ini = rep(0.03, ncol(mY)), beta_ini = rep(0.8, ncol(mY)), a_ini = 0.03, b_ini = 0.8, gamma_ini = rep(1, ncol(mY)), errorDist = 2, control = list()) increaseSim(x, nSim=10000) ## S3 method for class 'bayesDccGarch' window(x, start = NULL, end = NULL, thin = NULL, ...)
mY |
a matrix of the data (n \times k). |
nSim |
length of Markov chain. Default: |
tail_ini |
initial value of ν parameter if |
omega_ini |
a numeric vector (k \times 1) with the initial values of ω_i parameters. Default: |
alpha_ini |
a numeric vector (k \times 1) with the initial values of α_i parameters. Default: |
beta_ini |
a numeric vector (k \times 1) with the initial values of β_i parameters. Default: |
a_ini |
a numeric value of the initial values of a parameter. Default: |
b_ini |
a numeric value of the initial values of b parameter. Default: |
gamma_ini |
a numeric vector (k \times 1) with the initial values of γ_i parameters. Default: |
errorDist |
a probability distribution for errors. Use |
control |
list of control arguments (See *Details*). |
x |
an object of |
start |
the first iteration of interest from Markov chain. |
end |
the last iteration of interest from Markov chain. |
thin |
the required interval between successive samples. |
... |
additional arguments for S3 generic |
The bayesDccGarch()
function performs a Markov Chain for all parameters of the model DCC-GARCH(1,1) (or GARCH(1,1) in the univariate case).
There are three options of probability distributions for the error
component. These are the standardized skew versions of normal, t-student and ged distributions. See Fioruci et al (2014a) and Fioruci et al (2014b) for any detail.
The control
argument can be used for define the prior hyper-parameters and the simulation algorithm parameters.
It is a list that can supply any of the following components:
the value of hyper-parameter μ_ν if errorDist=2
or the hyper-parameter μ_δ if errorDist=3
. Default: 8
a vector with the hyper-parameters μ_{γ_i}. Default: rep(0,ncol(mY)
a vector with the hyper-parameters μ_{ω_i}. Default: rep(0,ncol(mY)
a vector with the hyper-parameters μ_{α_i}. Default: rep(0,ncol(mY)
a vector with the hyper-parameters μ_{β_i}. Default: rep(0,ncol(mY)
the value of the hyper-parameter μ_a. Default: 0
the value of the hyper-parameter μ_b. Default: 0
the value of hyper-parameter σ_ν if errorDist=2
or the hyper-parameter σ_δ if errorDist=3
. Default: 10
a vector with the hyper-parameters σ_{γ_i}. Default: rep(1.25,ncol(mY)
a vector with the hyper-parameters σ_{ω_i}. Default: rep(10,ncol(mY)
a vector with the hyper-parameters σ_{α_i}. Default: rep(10,ncol(mY)
a vector with the hyper-parameters σ_{β_i}. Default: rep(10,ncol(mY)
the value of the hyper-parameter σ_a. Default: 10
the value of the hyper-parameter σ_b. Default: 10
the random walk Metropolis-Hasting algorithm update. Use 1
for update all parameters as one block,
use 2
for update one parameter for each time and use 3
for an automatic choice.
number of simulation for pilot sample if control$simAlg=3
. Default:1000
the cholesky decomposition matrix of the covariance matrix for simulation by one-block Metropolis-Hasting. It must to be passed if control$simAlg=1
.
a vector with the standard deviations for simulation by one-dimensional Metropolis-Hasting. It must to be passed if control$simAlg=2
.
a logical variable for if the function should report the number of interactions in each 100 interactions or not. Default: TRUE
The function increaseSim()
can be used to increase the length of Markov chain simulation.
The function window()
can be used to filter the Markov chain simulation. In this case, all statistics are recomputed.
An object of bayesDccGarch
class, which contains a list with elements:
$control |
a list with the used |
$MC |
a element of |
$H |
a matrix with the Bayesian estimates of volatilities and co-volatilities. |
$IC |
the Bayesian estimate of Akaike Information Criterion, Bayesian Information Criterion and Deviance Information Criterion. |
$elapsedTime |
an object of class |
Jose Augusto Fiorucci, Ricardo Sandes Ehlers and Francisco Louzada
Fioruci, J.A., Ehlers, R.S., Andrade Filho, M.G. Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions, Journal of Applied Statistics, 41(2), 320–331, 2014a. http://dx.doi.org/10.1080/02664763.2013.839635.
Fioruci, J.A., Ehlers, R.S., Louzada, F. BayesDccGarch - An Implementation of Multivariate GARCH DCC Models, ArXiv e-prints, 2014b. http://adsabs.harvard.edu/abs/2014arXiv1412.2967F.
bayesDccGarch-package
, logLikDccGarch
, plot
, plotVol
data(DaxCacNik) Dax = DaxCacNik[,1] ### DCC-GARCH(1,1) ### out = bayesDccGarch(DaxCacNik[1:10,], nSim=1000) # more data is necessary summary(out) plot(out) ### GARCH(1,1) ### # out = bayesDccGarch(Dax) # summary(out) # plot(out) ### DCC-GARCH(1,1) with SSGED innovations ### ## out = bayesDccGarch(DaxCacNik, tail_ini=1.5, errorDist=3) ### Informative Prior for alpha and beta parameters ### # out = bayesDccGarch(Dax, alpha_ini=0.01, beta_ini=0.90, # control=list(mu_alpha=0.01, sigma_alpha=0.001, mu_beta=0.90, sigma_beta=0.001)) # summary(out) # plot(out$MC) ## plot Markov Chain # plot(out) ### more simulations ################################### # out1 = bayesDccGarch(DaxCacNik) # out2 = increaseSim(out, 10000) # more 10000 simulations # out3 = window(out2, start=5000) # removing the first 5000 as burning # summary(out3) # ### Plotting volatilities # # plot(out3) # ### Plotting Markov Chain # # plot(out3$MC) # ########################################################