t-copula and various measures of dependance

The t-copula can use Spearman's rho to describe the dependance between the variables. To build the all important intuition a graph helps clear things up.

One really sees how the copula takes into account the relationship from a very negative dependance (when one rises the other falls, rho < 0), via a neutral relationship (one rises, the other is not incluenced, rho=0), to a strong positive relationship (one rises, the other rises as well, rho > 0).








Try it out in R:

  library("copula")

  rho_list <- c(-0.9, -0.7, -0.5, -0.3, 0, 0.3, 0.5, 0.7, 0.9)

  par(mfrow=c(3,3))
  for(i in 1:length(rho_list)){
    rho <- rho_list[i]
    t.cop    <- tCopula(c(rho), dim=2, dispstr="ex", df=3)
    persp(t.cop, dcopula, col='lightblue', main=paste("rho", rho), 
          phi=20, xlab='U', ylab='V', zlab='tCopula', n=30)
  }