I am new to copula and I would like figure out how to find the log-likelihood function of Clayton copula and the expectation (log-likelihood function)? Any help please?
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$\begingroup$ While I have no access to it right now, this SAS help page points to Cherubini, U., Luciano, E., & Vecchiato, W. (2004). Chapter 7. In Copula methods in finance. John Wiley & Sons. $\endgroup$– FirebugSep 13, 2016 at 11:36
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$\begingroup$ Thank you for the help page, yes they figure out the equation. That is great. $\endgroup$– user130885Sep 13, 2016 at 12:03
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You can find the density for the Clayton copula in this document. So, the log-likelihood, having observations $\{x_1,\ldots,x_n\}$ where $x_i = (u_i,v_i)$ is $$\ell(\delta,x) = \sum_{i=1}^n \log c(x_i, \delta).$$
