dcc_estimation: Estimating an (E)DCC-GARCH model
In ccgarch: Conditional Correlation GARCH models

Description Usage Arguments Value Note References See Also Examples

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.

1 2	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.

The details of the first and second stage estimation are also saved in first and second, respectively.

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.sim

# 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")

## Not run: 
# 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

## End(Not run)

****************************************************************
*  Estimation has been completed.                              *
*  The outputs are saved in a list with components:            *
*    out    : the estimates and their standard errors          *
*    loglik : the value of the log-likelihood at the estimates *
*    h      : a matrix of estimated conditional variances      *
*    DCC    : a matrix of DCC estimates                        *
*    std.resid : a matrix of the standardised residuals        *
*    first  : the results of the first stage estimation        *
*    second : the results of the second stage estimation       *
****************************************************************
                    a1          a2          a3         A11        A22
estimates 0.0031825039 0.004874008 0.001542922 0.193579143 0.29856078
std.err   0.0008796319 0.036548922 0.044322349 0.001149049 0.04950524
                 A33          B11        B22        B33   dcc alpha   dcc beta
estimates 0.14630728 0.7382394822 0.58599949 0.76419059 0.008188539 0.96809739
std.err   0.05859898 0.0005114075 0.03271361 0.05123449 0.005416799 0.02734128