estimateDCC: Estimating DCC-GARCH model
In ccgarch2: Conditional Correlation GARCH Models

Description Usage Arguments Details Value References See Also Examples

This function estimates a Dynamic Conditional Correlation GARCH model.

estimateDCC(inia = NULL, iniA = NULL, iniB = NULL, ini.dcc = NULL, 
      data, model="diagonal", ...)

## S3 method for class 'dcc'
print(x, ...)

`inia`	a vector of initial values in the GARCH part.
`iniA`	a square or diagonal matrix of initial values for the ARCH parameter matrix in the GARCH part.
`iniB`	a square or diagonal matrix of initial values for the GARCH parameter matrix in the GARCH part.
`ini.dcc`	a vector of length 2 initial parameters for the cDCC part.
`data`	a data frame or a matrix object containing the variables.
`model`	a chacacter string setting the GARCH part of the model.
`x`	an object of class `"dcc"`.
`...`	optional arguments. Currently not in use.

This function estimates a Dynamic Conditional Correlation (DCC-) GARCH model of Engle (2002).

The extractor function summary() is available for a "dcc" class object displaying a table with estimates and inferencial statistics, information criterion and some diagnostic results of the standardized residuals. See summary.dcc for details.

Estimation of the model is carried out in two steps. The optimization in both steps is implemented by solnp function in Rsolnp package and its outcome is save ‘as is’ in a list component f.stage and s.stage, respectively.

solnp uses a sequencial quadratic programming (SQP) technique to optimize the objective function. See the manual and the references therein for details. During the optimization, positivity and stationarity restrictions are imposed on the parameters.

Rsonlp has a function called gosolnp that generates initial starting values randomly. A logical argument random controlls which function to use in the optimization. The default is random = FALSE meaning that solnp of Rsolnp is used. If random = TRUE, gosolnp is used. It should be noted that optimization takes longer time and may not always be successful when gosolnp is used.

This function returns an S3 class object "dcc" that is a list with the following components.

`f.stage`	an output of the first stage optimization from Rsolnp.
`s.stage`	an output of the second stage optimization from Rsolnp.
`model`	a chacacter string setting the GARCH part of the model.
`method`	the optimization method used.
`initial`	a list with the initial parameter vectors/matrices. The included components are `a`, `A`, `B`, and `dcc.par`.
`data`	the data matrix. Returned as a zoo object.
`DCC`	a matrix of the conditional correlations. Each row corresponds to vec(R_t). Returned as a zoo object.
`h`	a matrix of the conditional variances. Each row corresponds to h_t. Returned as a zoo object.
`z`	a matrix of the standardized residuals. Each row corresponds to z_t. Returned as a zoo object.

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.

summary.dcc, simulateDCC, plot.dcc, optim

## Not run: 
ndim <- 3
nobs <- 3000

## Setting parameters in the DCC part
a <- 0.05
b <- 0.8

## Setting a correlation matrix
Q <- diag(0, ndim)
Q[lower.tri(Q)] <- c(0.8, 0.3, 0.1)
Q <- Q + t(Q)
diag(Q) <- 1

## setting parameters in the GARCH part
a0 <- c(0.05, 0.07, 0.1)
A <- matrix(c(0.06, 0.0, 0.0, 0.07, 0.08, 0.002, 0.003, 0.0, 0.06), 
    ndim, ndim)
B <- matrix(c(0.75, 0.09, 0.03, 0.001, 0.81, 0.003, 0.001, 0.008, 0.84), 
    ndim, ndim)

## Simulating data
sim.data <- simulateDCC(a, b, Q, a0, diag(diag(A)), diag(diag(B)), nobs)

## Estimating a DCC model
garch_dcc <- estimateDCC(inia=a0, iniA=diag(diag(A)), iniB=diag(diag(B)), 
    ini.dcc=c(a, b), data=sim.data$eps, model="diagonal")

## Summarizing the results
summary_garch_dcc <- summary(garch_dcc)

## Plotting items
plot(garch_dcc, item="correlation")   # for dynamic conditional correlations
plot(garch_dcc, item="volatility")    # for volatility (square root of conditional variance)
plot(garch_dcc, item="std.residuals") # for satandardized residuals
plot(garch_dcc, item="return")        # for return (original data)

## End(Not run)