Modified vine copula Bayesian information criterion (mBICv) — mBICV • rvinecopulib
Description: Calculates the modified vine copula Bayesian information criterion.

# Modified vine copula Bayesian information criterion (mBICv)

Source: `R/vinecop_methods.R`
`mBICV.Rd`

Calculates the modified vine copula Bayesian information criterion.

    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
    #> [1] 17.88
    mBICV(fit, 0.1) # with a 0.1 prior probability of a non-independence copula
    #> [1] 79.40229