estimateCCC: Estimating CCC-GARCH model
In ccgarch2: Conditional Correlation GARCH Models

Description Usage Arguments Details Value References See Also Examples

This function estimates a Constant Conditional Correlation GARCH model.

estimateCCC(inia = NULL, iniA = NULL, iniB = NULL, 
    data, model="diagonal", ...)

## S3 method for class 'ccc'
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.
`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 Constant Conditional Correlation (CCC-) GARCH model of Bollerslev (1990).

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

Estimation of the model is carried out in a single step, that is, the parameters in the GARCH part and the conditional correlations are simultaneously estimated. The optimization is implemented by solnp function in Rsolnp package and its outcome is save ‘as is’ in a list component results.

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.

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

`results`	an output of the optimization from `optim`.
`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`, and `B`.
`data`	the data matrix. Returned as a zoo object.
`estimates`	a list with the following components: `a` for constant, `A` for ARCH, `B` for GARCH parameters in the conditional variance equation, and `R` for the constant conditional correlation matrix.
`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.

Bollerslev, T. (1990), “Modeling the Coherence in Short-Run Nominal Exchange Rates: A Multivariate Generalized ARCH Approach”, Review of Economics and Statistics, 72, 498–505.

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.ccc, simulateCCC, plot.ccc, solnp

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

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

## Setting a correlation matrix
R <- diag(0, ndim)
R[lower.tri(R)] <- c(0.8, 0.3, 0.1)
R <- R + t(R)
diag(R) <- 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 <- simulateCCC(R, a0, diag(diag(A)), diag(diag(B)), nobs)

## Estimating a CCC model
garch_ccc <- estimateCCC(inia=a0, iniA=diag(diag(A)), iniB=diag(diag(B)), 
    data=sim.data$eps, model="diagonal")

## Summarizing the results
summary_garch_ccc <- summary(garch_ccc)

## Plotting items
plot(garch_ccc, item="correlation")   # this returns an error since correlation is constant
plot(garch_ccc, item="volatility")    # for volatility (square root of conditional variance)
plot(garch_ccc, item="std.residuals") # for satandardized residuals
plot(garch_ccc, item="return")        # for return (original data)

## End(Not run)