开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

Drink H · 2020年07月01日

问一道题：NO.PZ2020011101000036

  1. FRM I
  2. Quantitative

问题如下：

If an asset has zero skewness, what is the maximum kurtosis it can have to not reject normality with a sample size of 100 using a 5% test? What if the sample size is 2,500?

选项：

解释：

The Jarque-Bera has χ22\chi_2^2 distribution, and the critical value for a test with a size of 5% is 5.99. The Jarque-Bera statistic is

JB=(T−1)(S^2/6+(κ^−3)2/24)JB = (T - 1)(\widehat S^2/6+(\widehat\kappa-3)^2/24)

so that when the skewness S^=0\widehat S = 0 , the test statistic is (T−1)(κ^−3)2/24(T - 1)(\widehat\kappa-3)^2/24 .

In order to not reject the null, we need (T−1)(κ^−3)2/24(T - 1)(\widehat\kappa-3)^2/24 ≤ 5.99

and so (κ^−3)2≤24∗5.99/(T−1)(\widehat\kappa-3)^2 ≤ 24*5.99/(T-1)

and κ^≤3+24∗5.99/(T−1)\widehat\kappa ≤ 3+\sqrt {24*5.99/(T-1)} .

When T = 100, this value is 4.20. When T = 2,500 this value is 3.24. This shows that the JB test statistic is sensitive to even mild excess kurtosis.

"This shows that the JB test statistic is sensitive to even mild excess kurtosis."这句话怎么理解？

添加评论
1 个答案

袁园_品职助教 · 2020年07月02日

同学你好！

这句话就是说JB test 对kurtosis 的变化是很敏感的

就是说 K>3 时，哪怕只超过一点点，也会对JB test 产生较大影响

  • 1

    回答

  • 0

    关注

  • 441

    浏览
相关问题

NO.PZ2020011101000036 问题如下 If asset hzero skewness, whis the maximum kurtosis it chave to not rejenormality with a sample size of 100 using a 5% test? Whif the sample size is 2,500? The Jarque-Bera hχ22\chi_2^2χ22​ stribution, anthe criticvalue for a test with a size of 5% is 5.99. The Jarque-Bera statistic isJB=(T−1)(S^2/6+(κ^−3)2/24)JB = (T - 1)(\wihS^2/6+(\wihat\kappa-3)^2/24) JB=(T−1)(S2/6+(κ−3)2/24)so thwhen the skewness S^=0\wihS = 0 S=0, the test statistic is (T−1)(κ^−3)2/24(T - 1)(\wihat\kappa-3)^2/24 (T−1)(κ−3)2/24.In orr to not rejethe null, we nee(T−1)(κ^−3)2/24(T - 1)(\wihat\kappa-3)^2/24 (T−1)(κ−3)2/24 ≤ 5.99anso (κ^−3)2≤24∗5.99/(T−1)(\wihat\kappa-3)^2 ≤ 24*5.99/(T-1) (κ−3)2≤24∗5.99/(T−1)anκ^≤3+24∗5.99/(T−1)\wihat\kappa ≤ 3+\sqrt {24*5.99/(T-1)} κ≤3+24∗5.99/(T−1)​.When T = 100, this value is 4.20. When T = 2,500 this value is 3.24. This shows ththe JB test statistic is sensitive to even milexcess kurtosis. 请问为什么自由度不是样本数量-1呢，之前第三章的时候一直都是用的样本个数-1

2024-06-06 10:45 1 · 回答

请教老师，为什么chi-square table选取自由度为2 的5%？

2020-03-09 07:13 2 · 回答