Copula-based measures of asymmetry between the lower and upper tail probabilities
| Autor: | Kato, Shogo, Yoshiba, Toshinao, Eguchi, Shinto |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We propose a copula-based measure of asymmetry between the lower and upper tail probabilities of bivariate distributions. The proposed measure has a simple form and possesses some desirable properties as a measure of asymmetry. The limit of the proposed measure as the index goes to the boundary of its domain can be expressed in a simple form under certain conditions on copulas. A sample analogue of the proposed measure for a sample from a copula is presented and its weak convergence to a Gaussian process is shown. Another sample analogue of the presented measure, which is based on a sample from a distribution on $\mathbb{R}^2$, is given. Simple methods for interval estimation and nonparametric testing based on the two sample analogues are presented. As an example, the presented measure is applied to daily returns of S&P500 and Nikkei225. Comment: 25 pages |
| Databáze: | arXiv |
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