[R] Error : 'start' contains NA values when fitting frank copula

[Martin Maechler]

>>>>> Soumen Banerjee <soumen08 using gmail.com>
>>>>>     on Sat, 21 Apr 2018 17:22:56 +0800 writes:

    > Hello!  I am trying to fit a copula to some data in R and
    > I get the error mentioned above. This is the code for a
    > reproducible example -

(not really reproducible: You did not set the random seed, so
 the data is different every time;
 OTOH, yes, the following always gives an error)

    > library(copula)

Slightly clearer showing what you are doing:

    x <- runif(200)
    data <- cbind(x, 2*x, 3*x)

    > fr_cop = frankCopula(dim=3)
    > fit_fr_cop = fitCopula(fr_cop, pobs(data), method = "mpl") #Error Here

    > The error says : Error in fitCopula.ml(copula, u = data, method = method,
    > start = start, : 'start' contains NA values

    > What could be going wrong?

Is this a homework question? [probably not, but ..]

The homework question & answer would be

Q:  What is the best fitting 3D copula if you have perfectly
    correlated ("rank 1") data?

A:  The complete-dependence copula ... which is indeed a boundary case,
    hard to imagine you'd encounter for non-artifical data.

Another hint:

> fitCopula(normalCopula(,3), pobs(data))
Call: fitCopula(copula, data = data)
Fit based on "maximum pseudo-likelihood" and 200 3-dimensional observations.
Copula: normalCopula 
rho.1 
    1 
The maximized loglikelihood is 3686 
Optimization converged
>
-----------

Yes, one could adapt the fitCopula() code to work better for
this extreme boundary case,
and for the Frank copula,  it would return

> fitCopula(frankCopula(,3), pobs(data))
Call: fitCopula(copula, data = data)
Fit based on "maximum pseudo-likelihood" and 200 3-dimensional observations.
Copula: frankCopula 
   alpha 
7.21e+16 
The maximized loglikelihood is 1.798e+308 
Optimization converged


but it would need even more tweaking to also give such
  "alpha ~= +Inf"
results for other cases such as Gumbel or Joe.

I may add the possibility for frank*() as shown above for the
next release of the copula package...
but am a bit hesitant to complicate (and slowdown) the current
code by adding an extra check for this situation.

Martin Maechler
ETH Zurich