Simulate DCC-GARCH Data with Higher-Order Support

Simulate realistic multivariate time series data from a DCC(q,p)-GARCH process. Supports arbitrary DCC orders through vector-valued alpha_dcc and beta_dcc. This function is primarily intended for testing and examples.

Usage

simulate_dcc_garch(
  n,
  k = 2,
  omega = c(0.05, 0.08),
  alpha_garch = c(0.1, 0.12),
  beta_garch = c(0.85, 0.82),
  alpha_dcc = 0.04,
  beta_dcc = 0.93,
  Qbar = NULL,
  seed = NULL
)

Arguments

n

Integer number of observations to simulate

k

Integer number of series (default: 2)

omega

Numeric vector of length k: GARCH intercepts (default: c(0.05, 0.08))

alpha_garch

Numeric vector of length k: ARCH effects (default: c(0.10, 0.12))

beta_garch

Numeric vector of length k: GARCH effects (default: c(0.85, 0.82))

alpha_dcc

Numeric scalar or vector: DCC alpha parameters. Length determines q (number of alpha lags). (default: 0.04)

beta_dcc

Numeric scalar or vector: DCC beta parameters. Length determines p (number of beta lags). (default: 0.93)

Qbar

Matrix (k x k): Unconditional correlation matrix. If NULL, uses moderate correlation (0.5 off-diagonal)

seed

Integer random seed for reproducibility

Value

A matrix of dimension (n x k) with simulated returns

Details

The function simulates data from the DCC(q,p)-GARCH model: $$y_{i,t} = \sqrt{h_{i,t}} z_{i,t}$$ $$h_{i,t} = \omega_i + \alpha_i y_{i,t-1}^2 + \beta_i h_{i,t-1}$$ $$Q_t = \bar{Q}(1-\sum\alpha-\sum\beta) + \sum_{j=1}^{q} \alpha_j z_{t-j}z_{t-j}' + \sum_{j=1}^{p} \beta_j Q_{t-j}$$ $$R_t = \text{diag}(Q_t)^{-1/2} Q_t \text{diag}(Q_t)^{-1/2}$$

where \(z_t \sim N(0, R_t)\).

For backward compatibility, scalar alpha_dcc and beta_dcc produce DCC(1,1). To simulate DCC(q,p), provide alpha_dcc as vector of length q and beta_dcc as vector of length p.

Examples

if (FALSE) { # \dontrun{
# Simulate 500 observations with default DCC(1,1) parameters
y <- simulate_dcc_garch(n = 500, seed = 42)

# DCC(1,2): one alpha lag, two beta lags
y_dcc12 <- simulate_dcc_garch(
  n = 300,
  alpha_dcc = 0.05,
  beta_dcc = c(0.50, 0.40),
  seed = 123
)

# DCC(2,2): two lags each
y_dcc22 <- simulate_dcc_garch(
  n = 300,
  alpha_dcc = c(0.03, 0.02),
  beta_dcc = c(0.50, 0.40),
  seed = 456
)

# Constant correlation (set alpha_dcc = 0)
y_const <- simulate_dcc_garch(n = 200, alpha_dcc = 0, beta_dcc = 0, seed = 789)
} # }