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

## Description

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.

## Usage

 1 2  dcc.estimation(inia, iniA, iniB, ini.dcc, dvar, model, method="BFGS", gradient=1, message=1) 

## Arguments

 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)

## Value

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

## Note

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.

## 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.

dcc.sim

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 # 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) 

### Example output

****************************************************************
*  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


ccgarch documentation built on May 29, 2017, 12:58 p.m.