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Copula GARCH Weighted Estimation (Two-Stage)

estimate_garch_weighted_cgarch.Rd

Implements weighted MLE for Copula GARCH models. Stage 1: Estimate univariate GARCH parameters for each series Stage 2: Estimate copula dependence parameters (DCC dynamics + shape)

Usage

estimate_garch_weighted_cgarch(
  residuals,
  weights,
  spec,
  diagnostics = NULL,
  iteration = NULL,
  state = NULL,
  verbose = FALSE,
  dcc_threshold = 0.02,
  dcc_criterion = "bic",
  force_constant = FALSE
)

Arguments

residuals

Matrix of residuals (T x k)

weights

Vector of observation weights (length T)

spec

Model specification list containing:

  • garch_spec_fun: "cgarch_modelspec"

  • garch_spec_args: list with dcc_order, dynamics, transformation, copula, garch_model (univariate specs)

  • start_pars: starting parameter values

  • distribution: copula distribution ("mvn" or "mvt")

diagnostics

Optional diagnostics collector object

iteration

Current EM iteration number

state

Current regime state index

verbose

Logical; print diagnostic information

dcc_threshold

Threshold for DCC degeneracy detection (default 0.02)

dcc_criterion

Selection criterion for constant vs dynamic ("bic", "aic", "threshold")

force_constant

Logical; if TRUE, skip dynamic estimation

Value

List with:

  • coefficients: list with garch_pars, dcc_pars, dist_pars, correlation_type

  • warnings: list of warning messages

  • diagnostics: updated diagnostics object

Details

The Copula GARCH model differs from DCC in how it handles the dependence structure:

  1. Marginal Transformation: Standardized residuals are transformed to uniform [0,1] margins via probability integral transform (PIT). The transformation can be:

    • "parametric": Uses the estimated univariate distribution's CDF

    • "empirical": Uses the empirical CDF

    • "spd": Uses semi-parametric distribution (see fit_spd_transform)

  2. Copula Specification: The uniform margins are then transformed according to the copula distribution:

    • "mvn": Multivariate Normal copula (Gaussian copula)

    • "mvt": Multivariate Student-t copula

  3. Correlation Dynamics: Same as DCC - can be "constant", "dcc", or "adcc" For ADCC, see adcc_recursion.

This function is called by the M-step of the EM algorithm in fit_ms_varma_garch when garch_spec_fun = "cgarch_modelspec".

See also