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CCC-GARCH Simulation Inputs and Model Variants

Article Quant Q&A · Author: Efi
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Summary

This document describes an R function for simulating multivariate constant conditional correlation GARCH processes. It distinguishes the original CCC model, where ARCH and GARCH parameter matrices are diagonal, from an extended version that permits full matrices with off-diagonal effects. Innovations can follow a normal or Student's t distribution, while the correlation matrix is held constant over time.

The description lists the function's required inputs: observation count, variance-equation constants, ARCH and GARCH matrices, correlation matrix, degrees of freedom, burn-in length, and a model selector. It does not explain how to estimate GARCH coefficients or construct those inputs, despite the question asking about automatic coefficient calculation. No empirical results or estimation guidance are provided, so the material is useful mainly as a concise reference to simulation setup and model specification.

Key ideas

  • The original CCC-GARCH specification uses diagonal ARCH and GARCH parameter matrices.
  • The extended CCC-GARCH version allows full parameter matrices with off-diagonal effects.
  • The simulation supports normal and Student's t innovations.
  • The function requires the user to supply model parameters and a constant correlation matrix.

Tags

StatisticsVolatility
Full text
# Constant Conditional Correlation GARCH (1,1)


# Constant Conditional Correlation GARCH (1,1)












I am a beginner in R and my econometrics background is not very sound either. I want to build a constant conditional correlation GARCH (1,1) model in R and I found the function, the description of which I have copy-pasted below. This functions requires that you calculate the individual matrices and vectors individually and then you plug them into the function. The problem is that I do not know how to do it individually. Is there any package that calculates the GARCH coefficients automatically?

Thanks a lot!

Simulating an (E)CCC-GARCH(1,1) process

Description

This function simulates data either from the original CCC-GARCH by Bollerslev (1990) or from the Extended CCC-GARCH that has non-zero off-diagonal entries in the parameter matrices in the GARCH equation. The innovations (the standardised residuals) can be either a normal or student's $t$ distribution.

The dimension (N) is determined by the number of elements in the \mathbf{a} vector.

Usage

eccc.sim(nobs, a, A, B, R, d.f=Inf, cut=1000, model) Arguments

nobs a number of observations to be simulated (T)

a a vector of constants in the GARCH equation (N \times 1)

A an ARCH parameter matrix in the GARCH equation. \mathbf{A} can be a diagonal matrix for the original CCC-GARCH model or a full matrix for the extended model (N \times N)

B a GARCH parameter matrix in the GARCH equation. \mathbf{B} can be a diagonal matrix for the original CCC-GARCH model or a full matrix for the extended model (N \times N)

R a constant conditional correlation matrix (N \times N)

d.f the degrees of freedom parameter for the t-distribution

cut the number of observations to be thrown away for removing initial effects of simulation

model a character string describing the model. "diagonal" for the diagonal model and "extended" for the extended (full ARCH and GARCH parameter matrices) model

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.