Simulate CGARCH Data with ADCC Support

Simulate data from a Copula-GARCH process with DCC or ADCC dynamics.

Usage

simulate_cgarch(
  n,
  k = 2,
  omega = NULL,
  alpha_garch = NULL,
  beta_garch = NULL,
  alpha_dcc = 0.04,
  beta_dcc = 0.93,
  gamma_dcc = NULL,
  copula = "mvn",
  shape = 8,
  Qbar = NULL,
  seed = NULL
)

Arguments

n

Integer number of observations

k

Integer number of series (default: 2)

omega

Numeric vector of GARCH omega parameters (length k)

alpha_garch

Numeric vector of GARCH alpha parameters (length k)

beta_garch

Numeric vector of GARCH beta parameters (length k)

alpha_dcc

Numeric: DCC alpha parameter (default: 0.04)

beta_dcc

Numeric: DCC beta parameter (default: 0.93)

gamma_dcc

Numeric: ADCC gamma parameter for leverage (default: NULL for standard DCC)

copula

Character: copula type ("mvn" or "mvt")

shape

Numeric: degrees of freedom for MVT copula (default: 8)

Qbar

Matrix: unconditional correlation matrix. If NULL, uses moderate correlation.

seed

Integer random seed

Value

Matrix of simulated returns (n x k)

Details

When gamma_dcc is provided (non-NULL and non-zero), the function simulates from an ADCC (Asymmetric DCC) process where negative shocks have a larger impact on correlation dynamics:

Q_t = Omega + alpha * (z_t-1 z't-1) + gamma * (nt-1 n't-1) + beta * Qt-1

where n_t = z_t * I(z_t < 0) captures negative shocks only.