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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.14349 |
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| _version_ | 1866913437815144448 |
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| author | Koike, Takaaki Kato, Shogo Yoshiba, Toshinao |
| author_facet | Koike, Takaaki Kato, Shogo Yoshiba, Toshinao |
| contents | We call two copulas tail equivalent if their first-order approximations in the tail coincide. As a special case, a copula is called tail symmetric if it is tail equivalent to the associated survival copula. We propose a novel measure and statistical test for tail equivalence. The proposed measure takes the value of zero if and only if the two copulas share a pair of tail order and tail order parameter in common. Moreover, taking the nature of these tail quantities into account, we design the proposed measure so that it takes a large value when tail orders are different, and a small value when tail order parameters are non-identical. We derive asymptotic properties of the proposed measure, and then propose a novel statistical test for tail equivalence. Performance of the proposed test is demonstrated in a series of simulation studies and empirical analyses of financial stock returns in the periods of the world financial crisis and the COVID-19 recession. Our empirical analysis reveals non-identical tail behaviors in different pairs of stocks, different parts of tails, and the two periods of recessions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measuring and testing tail equivalence Koike, Takaaki Kato, Shogo Yoshiba, Toshinao Methodology 60E05, 62E15, 62E20, 62G32 We call two copulas tail equivalent if their first-order approximations in the tail coincide. As a special case, a copula is called tail symmetric if it is tail equivalent to the associated survival copula. We propose a novel measure and statistical test for tail equivalence. The proposed measure takes the value of zero if and only if the two copulas share a pair of tail order and tail order parameter in common. Moreover, taking the nature of these tail quantities into account, we design the proposed measure so that it takes a large value when tail orders are different, and a small value when tail order parameters are non-identical. We derive asymptotic properties of the proposed measure, and then propose a novel statistical test for tail equivalence. Performance of the proposed test is demonstrated in a series of simulation studies and empirical analyses of financial stock returns in the periods of the world financial crisis and the COVID-19 recession. Our empirical analysis reveals non-identical tail behaviors in different pairs of stocks, different parts of tails, and the two periods of recessions. |
| title | Measuring and testing tail equivalence |
| topic | Methodology 60E05, 62E15, 62E20, 62G32 |
| url | https://arxiv.org/abs/2407.14349 |