I've developed a step by step procedure for estimating a copula based upon 2 stock time series returns but I don't understand and have not implemented one step that is discussed in most of the copula literature. Could someone please show me how to implement that step (#3), if it is necessary?

Step 1- Calculate the returns of each stock and then normalize using the Z-scores.

Step 2- Choose a suitable distribution for each stock, fit the distributions using MLE methods. I am calling the output of this step the marginals.

Step 3- (this is the step I don't understand on how to implement) Use the inverse probability transform or a uniform distribution transformation.

Step 4- Choose an appropriate copula, calculate its parameters using Kendall tau and/or other parameters. Use the marginals from step 2 OR should I be using output from step 3?



You're mixing steps of the estimation and application procedures of copula.

One way to estimate copula is to calculate the Kendal or Spearman correlation coefficients on the return series. There's no need to get marginals or standardize the series. You can use the correlation coefficients to estimate the copula's correlation matrix. For instance, if you use Gaussian copula and think that your margianals are normal, then you could even use the Pearson's correlation. Anyhow, there's a way to convert the correlations into Copula's correlation matrix.

when you actually apply copula to Monte Carlo or other problems, you need (inverse) marginals. Copula will generate correlated uniform random series, which you'll plug into your inverse marginals to get the correlated series. See this example in MATLAB it's self-explanatory.

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    $\begingroup$ Thanks for the response. It indicates that I need to revisit my understanding of the copula estimation process! $\endgroup$ – user4796756 Sep 16 '15 at 18:40
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    $\begingroup$ @user4796756, I would run the examples from the MATLAB docs, which I showed. They;re very simple to implement in R or other language. Once you run the examples, it'll all be very clear. $\endgroup$ – Aksakal Sep 16 '15 at 18:41

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