dcc.estimation: Estimating an (E)DCC-GARCH model

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

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:
outthe parameter estimates and their standard errors
loglikthe value of the log-likelihood at the estimates
ha matrix of the estimated conditional variances $(T \times N)$
DCCa matrix of the estimated dynamic conditional correlations $(T \times N^{2})$
std.resida matrix of the standardised residuals $(T \times N$). See Note.
firstthe results of the first stage estimation
secondthe results of the second stage estimation

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.

Examples

Run this code

# 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