24.8 How to Select Copula Given Dataset

Plot the percentile plot to diagnose

Calculate the empirical tail concentration function (LR function) and you can see how each copula fit best

Note: Figure 3.3.5 and 3.3.6 is not very good as it mix the underlying distn with the copula

24.8.1 Multivariate Copulas

Many options of copulas for 2 variables (pair-wise) but not multivariate

Normal and t-copula are the only well known multivariate copulas

Parameters: full correlation matrix

Normal copula

  • Has no correlation deep in the tail

  • The right tail concentration is very small, and approaches 0 at the limit

  • Just to be clear, the density deep in the tail (z > 0.999) you get very high values still

t-copula

  • Can be very strongly correlated in the tails, controlled with \(n\)

  • \(n \rightarrow \infty\), the t-copula approaches the normal copula

  • For small n, it has high density in the tails

  • T-copula also have some density in the other corners

    • Where on variable is high, the other is low