Negative log-likelihood of the Gaussian-copula marginal regression

The likelihood underlying fit_copula(): continuous Kumaraswamy or beta margins, serial dependence induced by a Gaussian copula with ARMA(p,q) structure on the latent (probit-transformed) scale. Evaluated in closed form via the innovations decomposition (no explicit construction or inversion of the n x n correlation matrix).

Usage

nll_copula(par, y, X, Z, p, q, family = "kuma", tau = 0.5)

Arguments

par

Numeric vector of parameters, in the order: location-submodel coefficients (length ncol(X)), shape-submodel coefficients (length ncol(Z)), AR coefficients (length p), MA coefficients (length q).

y

Numeric response vector in (0, 1).

X

Location-submodel design matrix.

Z

Shape-submodel design matrix.

p, q

Non-negative integers, the ARMA orders.

family

"kuma" (default) or "beta".

tau

Quantile level for the Kumaraswamy margin (ignored if family = "beta").

Value

The negative log-likelihood, a single number (1e10 as a penalty for parameter values outside the admissible region, e.g. a non-stationary ARMA polynomial).

See also

fit_copula()