dcc.estimation {ccgarch} | R Documentation |
This function carries out the two step estimation of the (E)DCC-GARCH model and returns estimates, standardised residuals, the estimated conditional variances, and the dynamic conditional correlations.
dcc.estimation(inia, iniA, iniB, ini.dcc, dvar, model, method="BFGS", gradient=1, message=1)
inia |
a vector of initial values for the constants in the GARCH equation
length(inia)=N |
iniA |
a matrix of initial values for the ARCH parameter matrix (N times N) |
iniB |
a matrix of initial values for the GARCH parameter matrix (N times N) |
ini.dcc |
a vector of initial values for the DCC parameters (2 times 1) |
dvar |
a matrix of the data (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 |
method |
a character string specifying the optimisation method in optim .
There are three choices, namely, Nelder-Mead ,
BFGS (default) and CG . |
gradient |
a switch variable that determines the optimisation
algorithm in the second stage optimisation. If gradient=0
Nelder-Mead is invokded. Otherwise BFGS is used (default). |
message |
a switch variable to turn off the display of the message when
the estimation is completed. If message=0 , the message
is suppressed. Otherwise, the message is displayed (default) |
a list with components:
out |
the parameter estimates and their standard errors |
loglik |
the value of the log-likelihood at the estimates |
h |
a matrix of the estimated conditional variances (T times N) |
DCC |
a matrix of the estimated dynamic conditional correlations (T times N^{2}) |
std.resid |
a matrix of the standardised residuals (T times N). See Note. |
first |
the results of the first stage estimation |
second |
the results of the second stage estimation |
The standardised residuals are calculated by dividing the original
series dvar
by the estimated conditional standard deviations sqrt(h)
.
See Engle (2002), in particular the equations (2) and (14), for details.
dcc.estimation
calls dcc.estimation1
and dcc.estimation2
for the
first and second stage estimation, respectively.
The details of the first and second stage estimation are also saved.
The switch variable simulation
is useful when one uses dcc.estimation
for simulation.
It supresses the display of the completion message.
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.
dcc.estimation1
,
dcc.estimation2
,
loglik.dcc1
,
loglik.dcc2
,
vector.garch
,
dcc.est
# Simulating data from the original DCC-GARCH(1,1) process nobs <- 1000; cut <- 1000 a <- c(0.003, 0.005, 0.001) A <- diag(c(0.2,0.3,0.15)) B <- diag(c(0.75, 0.6, 0.8)) uncR <- matrix(c(1.0, 0.4, 0.3, 0.4, 1.0, 0.12, 0.3, 0.12, 1.0),3,3) dcc.para <- c(0.01,0.98) dcc.data <- dcc.sim(nobs, a, A, B, uncR, dcc.para, model="diagonal") # Estimating a DCC-GARCH(1,1) model dcc.results <- dcc.estimation(inia=a, iniA=A, iniB=B, ini.dcc=dcc.para, dvar=dcc.data$eps, model="diagonal") # Parameter estimates and their robust standard errors dcc.results$out