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I have a dataset of 9 variables and I want to fit a t-copula to them in order to construct a multivariate and after that resample from it. I am using Matlab.

rng default  % For reproducibility
[Rho, nu] = copulafit('t',[A B C D E F G H L],'Method', 'ML'); 
r = copularnd('t',Rho,nu,1000); % I resample 1000 sample from it

once resample I use the icdf to obtain the time series of the sample data

a = ksdensity(data(:,1),r(:,1),'function','icdf');
...
l = ksdensity(data(:,9),r(:,9),'function','icdf');

after this command i get a warning on the convergence such as:

Warning: Inverse CDF calculation did not converge for p = 0.001161. 

this happens for 3 out of 9 variables. Assuming a is working fine and l gives me the warning, for a the max and min values are aligned with those of the original raw data data(:,1), while for l they are about 1e+7. Which is non-sense. Therefore I have checked the original data, for data(:,1) and data(:,9) and look like this

enter image description here

enter image description here

the second looks very very heteroskedastic compared to the first so I assume a t-copula is not suitable for that. My questions then are:

is the copula a tool only for stationary time series? in case of high heteroskedasticity, is there a way to model it for example with a conditional copula?

I would prefer if you could refer to python or Matlab.

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I don't know if this will help solve your convergence issue, but a standard way of incorporating conditional heteroskedasticity in copula models is to build a copula-GARCH model. Each time series is first modelled with GARCH, and then the standardized innovations from the GARCH models of all the series are jointly modelled with a copula.

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  • $\begingroup$ ok thanks. In this way the innovations will be iid and a copula can fit well in such conditions, is that right? $\endgroup$
    – Luigi87
    Jun 15 '21 at 8:26
  • $\begingroup$ @Luigi87, yes, if the GARCH models for all series adequately capture their conditional heteroskedasticity, this will be the case. $\endgroup$ Jun 15 '21 at 8:43

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