Estimating an (E)CCC-GARCH model

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Description

This function estimates an (E)CCC-GARCH(1,1) model and returns estimates, estimated volatility and various diagnostic statistics.

Usage

1
      eccc.estimation(a, A, B, R, dvar, model, method="BFGS")

Arguments

a

initial values for constants (N \times 1)

A

initial values for an ARCH parameter matrix (N \times N)

B

initial values for a GARCH parameter matrix (N \times N)

R

initial values a constant conditional correlation matrix (N \times N)

dvar

a matrix of data used for (E)CCC-GARCH estimation (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.

Value

A list with components:

out

a (4 \times npar) matrix. The estimates are contained in the first row. The remaining rows report standard errors based on three different methods of estimating the asymptotic covariance matrix

h

the estimated conditional variances (T \times N)

std.resid

a matrix of the standardised residuals (T \times N). See Note.

opt

the detailed results of the optimisation

para.mat

vectorised parameter estimates

Note

The standardised residuals are calculated through dividing the original series by the estimated conditional standard deviations. See, for instance, p.303 of Bollerslev (1990) for details.

References

Bollerslev, T. (1990), “Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model”, Review of Economics and Statistics, 20, 498–505.

Nakatani, T. and T. Ter\"asvirta (2009), “Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model”, Econometrics Journal, 12, 147–163.

Nakatani, T. and T. Ter\"asvirta (2008), “Appendix to Testing for Volatility Interactions in the Constant Conditional Correlation GARCH Model” Department of Economic Statistics, Stockholm School of Economics, available at http://swopec.hhs.se/hastef/abs/hastef0649.htm.

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