Error in copulafit: using chol Matrix must be positive definite.

I am trying to fit t copula in MatLab to my data and my function is:

u = ksdensity(range_1,  range_1,'function','cdf');
v = ksdensity(range_2,  range_2,'function','cdf');

 %fit a t-copula to returns
rng default ; % For reproducibility
[Rho,nu] = copulafit('t',[u v],'Method','ApproximateML');

And I get an error that says:

   Error using chol
  Matrix must be positive definite.

Error in copulafit/approxProfileNLL_t (line 314)
        nll = negloglike_t(nu,chol(Rho),t_);

Error in copulafit>bracket1D (line 494)
oldnll = nllFun(bound);

Error in copulafit (line 126)
    [lowerBnd,upperBnd] = bracket1D(profileFun,lowerBnd,5); % 'upper', search ascending from 5

I understood that it happens due to chol() decomposition, but I don't know which parameters should be changed to overcome this problem. Any help would be appreciated.

data that I use has been attached to this question box.

Answer 1

[Ben Drebing]

The reason you are getting this error is that your data (range_1 and range_2) is too correlated. You can see this by running the command:

>> scatterhist(range_1, range_2);

The correlation between range_1 and range_2 is too strong for "copulafit". I would recommend trying some other method of fitting your data. However, if you still want to use "copulafit", to get around this error, you can add a little noise to range_1 and range_2.

So, after you load your data, do:

>> range_1 = range_1 + 0.5*(rand(251,1) - 0.5); % This will randomly shift each data point by some 
>> range_2 = range_2 + 0.5*(rand(251,1) - 0.5); % random value between -0.25 and 0.25

This will make it so your data isn't exactly linear allowing "copulafit" to fit it.