Modified vine copula Bayesian information criterion (mBICv)

Calculates the modified vine copula Bayesian information criterion.

Usage

mBICV(object, psi0 = 0.9, newdata = NULL)

Arguments

object: a fitted vinecop object.
psi0: baseline prior probability of a non-independence copula.
newdata: optional; a new data set.

Details

The modified vine copula Bayesian information criterion (mBICv) is defined as

$$BIC = -2 loglik + \nu log(n) - 2 \sum_{t=1}^{d - 1} (q_t log(\psi_0^t) - (d - t - q_t) log(1 - \psi_0^t)) $$

where $\mathrm{loglik}$ is the log-likelihood and $\nu$ is the (effective) number of parameters of the model, $t$ is the tree level $\psi_0$ is the prior probability of having a non-independence copula and $q_t$ is the number of non-independence copulas in tree $t$. The mBICv is a consistent model selection criterion for parametric sparse vine copula models.

References

Nagler, T., Bumann, C., Czado, C. (2019). Model selection for sparse high-dimensional vine copulas with application to portfolio risk. Journal of Multivariate Analysis, in press (http://arxiv.org/pdf/1801.09739)

Examples

u <- sapply(1:5, function(i) runif(50))
fit <- vinecop(u, family = "par", keep_data = TRUE)
mBICV(fit, 0.9) # with a 0.9 prior probability of a non-independence copula
#> [1] 17.66954
mBICV(fit, 0.1) # with a 0.1 prior probability of a non-independence copula
#> [1] 68.88675