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Compute Standard Errors for GOGARCH Models

gogarch_standard_errors.Rd

Computes standard errors for GOGARCH component GARCH parameters. GOGARCH differs from DCC/CGARCH in that it uses ICA decomposition followed by univariate GARCH on independent components. SE computation focuses on the component-level GARCH parameters.

Usage

gogarch_standard_errors(
  garch_pars,
  ica_info,
  residuals,
  weights,
  distribution = "norm",
  method = c("hessian", "sandwich")
)

Arguments

garch_pars

List of GARCH parameters for each component: Each element is a list with omega, alpha1, beta1, etc.

ica_info

ICA decomposition results (A, W, K matrices, S components)

residuals

Original residuals matrix (T x k)

weights

Observation weights (length T)

distribution

Component distribution: "norm", "std", "nig", "gh"

method

SE method: "hessian" (default) or "sandwich"

Value

List with:

component_se

List of SE for each component

vcov_blocks

Block-diagonal vcov matrix (component-wise)

valid

Logical: all SEs computed successfully

n_components

Number of components

method

Method used

Details

GOGARCH models the observation vector as: Y = A * S, where S contains independent components each following univariate GARCH. The log-likelihood decomposes as: $$LL = \sum_i LL_i(S_i; \theta_i) + \log|det(K)|$$

Standard errors are computed independently for each component's GARCH parameters using the component-wise Hessian. This is justified by the independence assumption of ICA.

Note: SEs for the ICA mixing matrix A are not provided as A is typically treated as a fixed transformation after ICA estimation.

See also

estimate_garch_weighted_gogarch, compute_gogarch_loglik_ms