mBICV {rvinecopulib}

Modified vine copula Bayesian information criterion (mBICv)

Description

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 (https://arxiv.org/pdf/1801.09739.pdf)

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
mBICV(fit, 0.1) # with a 0.1 prior probability of a non-independence copula