Negated CRPS for Student-t predictive distributions

Wrapper over scoringRules::crps_t. Positively oriented: higher = better. The dof > 2 constraint ensures finite variance, which is required for the CRPS to be well-defined for the t-distribution.

Usage

crps_std(mu, sigma, dof, x)

Arguments

mu

Numeric vector. Location parameters (conditional means).

sigma

Numeric vector. Scale parameters (conditional SDs, > 0).

dof

Numeric vector or scalar. Degrees of freedom (> 2). May be scalar if constant across all observations (e.g. estimated once per rolling window).

x

Numeric vector. Realised observations.

Value

Numeric vector of CRPS values in (-Inf, 0] (negated loss).

Details

Calls scoringRules::crps_t(y = x, df = dof, location = mu, scale = sigma) and negates. Use for GARCH(1,1)-std forecasts where dof is the estimated degrees-of-freedom parameter from ugarchroll.

Examples

if (requireNamespace("scoringRules", quietly = TRUE)) {
  crps_std(mu = c(0, 1), sigma = c(1, 2), dof = 5, x = c(0.2, 1.3))
}
#> [1] -0.2721493 -0.5310947