Compute Copula Residuals from Simulated CGARCH Data — compute_cgarch

Given simulated returns and known GARCH parameters, compute the standardized residuals, apply PIT transformation, and convert to copula residuals needed for CGARCH estimation.

Usage

compute_cgarch_residuals(
  y,
  omega,
  alpha_garch,
  beta_garch,
  transformation = "parametric",
  copula = "mvn",
  shape = 8
)

Arguments

y: T x k matrix of simulated returns
omega: Vector of GARCH omega parameters (length k)
alpha_garch: Vector of GARCH alpha parameters (length k)
beta_garch: Vector of GARCH beta parameters (length k)
transformation: PIT transformation type ("parametric", "empirical", "spd")
copula: Copula distribution ("mvn" or "mvt")
shape: Degrees of freedom for MVT copula (default 8)

Value

List with:

std_resid: T x k matrix of standardized residuals
u_matrix: T x k matrix of PIT-transformed uniforms
z_matrix: T x k matrix of copula residuals