A diagnostic test for specification of copulas under censorship

Abstract

We propose a copula specification test for copula-based multivariate survival models under censorship. This flexible test is applicable to both Archimedean and non-Archimedean copulas and provides useful pointers for alternative copula construction when a null distribution is rejected. It is shown to be consistent and asymptotically distribution free. We demonstrate its good finite sample performance via Monte Carlo simulations. We apply this test to an insurance dataset on losses and expenses. Our test rejects the hypothesis of Gaussian copula. Furthermore, its diagnostic information suggests an alternative copula specification that captures the extreme-value dependence exhibited in the data.

Keywords:

• Copula specification
• censorship
• smooth test
• survival analysis

JEL::

• C14
• C22
• G22

Additional information

Funding

Juan Lin acknowledges financial support from the National Natural Science Foundation of China (grant nos. 71501164, 71671150, 71571154 and 71631004).