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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？

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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

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