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Answer: The Jarque-Bera test only examines the skewness and kurtosis of a distribution.
## Explanation **B is correct.** The Jarque-Bera (JB) test is specifically designed to test whether sample data has the skewness and kurtosis matching a normal distribution. The test statistic is calculated using both skewness and kurtosis measures. **Why other options are incorrect:** - **A is incorrect:** The JB test statistic follows a Chi-squared distribution with 2 degrees of freedom, not a binomial distribution. - **C is incorrect:** The JB test does not involve Gaussian copulas. It directly tests sample skewness and kurtosis against their expected values under normality. - **D is incorrect:** The JB test statistic explicitly incorporates sample size in its formula: $$JB = \frac{n}{6} \left(S^2 + \frac{(K-3)^2}{4}\right)$$ where n is the sample size, S is sample skewness, and K is sample kurtosis. The JB test is widely used in financial risk management to test for normality in return distributions, which is important for many risk models that assume normal distribution of returns.
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A risk analyst is evaluating a dataset of weekly returns for a commodity index. The analyst decides to use the Jarque-Bera test to determine if the returns of the commodity index are normally distributed. Which of the following statements will the analyst find to be correct regarding the Jarque-Bera test?
A
The Jarque-Bera test statistic follows a binomial distribution.
B
The Jarque-Bera test only examines the skewness and kurtosis of a distribution.
C
The Jarque-Bera test requires that a Gaussian copula be applied to the return data before conducting the test.
D
The Jarque-Bera test statistic does not depend on the sample size of the return dataset.