Compute NLL Surface for CGARCH(1,1)

Compute the negative log-likelihood on a grid of (alpha, beta) values for a Copula GARCH model.

Usage

compute_cgarch_nll_surface(
  z_matrix,
  weights,
  Qbar,
  alpha_range = c(0.01, 0.2),
  beta_range = c(0.7, 0.98),
  n_grid = 50,
  copula = "mvn",
  shape = 8
)

Arguments

z_matrix

T x k matrix of copula residuals

weights

T-vector of observation weights

Qbar

k x k unconditional correlation matrix

alpha_range

Range for alpha (default c(0.01, 0.20))

beta_range

Range for beta (default c(0.70, 0.98))

n_grid

Number of grid points per dimension (default 50)

copula

Copula distribution ("mvn" or "mvt")

shape

Degrees of freedom for MVT (only used if copula="mvt")

Value

List with alpha_grid, beta_grid, nll_surface, and mle location