Kato Shogo, Yoshiba Toshinao, Eguchi Shinto
Institute of Statistical Mathematics, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562 Japan.
Graduate School of Management, Tokyo Metropolitan University, 18F 1-4-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005 Japan.
Stat Pap (Berl). 2022;63(6):1907-1929. doi: 10.1007/s00362-022-01297-w. Epub 2022 Mar 6.
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 , is given. Simple methods for interval and region estimation are presented. A simulation study is carried out to investigate the performance of the proposed sample analogues and methods for interval estimation. As an example, the presented measure is applied to daily returns of S&P500 and Nikkei225. A trivariate extension of the proposed measure and its sample analogue are briefly discussed.
The online version contains supplementary material available at 10.1007/s00362-022-01297-w.
我们提出了一种基于 copula 的二元分布上下尾概率不对称性度量。所提出的度量形式简单，作为一种不对称性度量具有一些理想的性质。在所给 copula 的某些条件下，当指标趋于其定义域边界时，所提出度量的极限可以用一种简单形式表示。给出了来自 copula 的样本的所提度量的样本类似物，并证明了其依分布弱收敛到一个高斯过程。还给出了基于来自(\mathbb{R})上分布的样本的所提度量的另一个样本类似物。提出了区间和区域估计的简单方法。进行了一项模拟研究，以考察所提样本类似物和区间估计方法的性能。作为一个例子，将所提度量应用于标准普尔 500 指数和日经 225 指数的日收益率。简要讨论了所提度量的三元扩展及其样本类似物。
在线版本包含可在 10.1007/s00362-022-01297-w 获取的补充材料。
