Compute Standard Errors for CGARCH Models
cgarch_standard_errors.RdComputes standard errors for Copula GARCH DCC parameters using numerical differentiation of the copula log-likelihood. Supports both Gaussian (MVN) and Student-t (MVT) copulas.
Usage
cgarch_standard_errors(
params,
z_matrix,
weights,
Qbar,
copula_dist = "mvn",
use_reparam = FALSE,
method = c("hessian", "sandwich")
)Arguments
- params
Parameter vector:
For MVN copula: c(alpha, beta)
For MVT copula: c(alpha, beta, shape)
- z_matrix
T x k matrix of copula residuals (transformed standardized residuals). These are the result of the PIT transformation followed by inverse normal/t quantile transform.
- weights
T-vector of observation weights
- Qbar
k x k unconditional covariance matrix of z_matrix
- copula_dist
Copula distribution: "mvn" or "mvt"
- use_reparam
Logical: parameters in (psi, phi) space?
- method
SE method: "hessian" (default) or "sandwich"
Value
List with:
- se
Standard errors
- vcov
Variance-covariance matrix
- params
Parameter values
- param_names
Parameter names
- method
Method used
- hessian
Hessian matrix (if method = "hessian")
- eigenvalues
Hessian eigenvalues (if method = "hessian")
Details
The copula log-likelihood differs from DCC in that it subtracts the marginal log-densities. For MVN copula: $$\ell_t = -0.5[\log|R_t| + z_t'R_t^{-1}z_t - z_t'z_t]$$
For MVT copula: $$\ell_t = c(\nu) - 0.5\log|R_t| - \frac{\nu+k}{2}\log(1 + q_t/(\nu-2)) - \sum_j \log f_t(z_{jt})$$ where \(f_t\) is the marginal Student-t density.