Answer: The Jarque-Bera test only takes into account the skewness and kurtosis of a distribution.

The Jarque-Bera test is a statistical test used to determine whether a dataset is normally distributed. It is based on the skewness and kurtosis of the data, which are measures of the asymmetry and the tailedness of the distribution, respectively. The test statistic for the Jarque-Bera test is calculated using the formula: \[ JB = n \times \left(\frac{S^2}{6} + \frac{(K - 3)^2}{24}\right) \] where \( n \) is the sample size, \( S \) is the sample skewness, and \( K \) is the sample kurtosis. The test statistic follows a chi-squared distribution with two degrees of freedom under the null hypothesis that the data are normally distributed. As the sample size increases, the test becomes more powerful, meaning it is more likely to detect non-normality if it is present. Option A is incorrect because the Jarque-Bera test statistic follows a chi-squared distribution, not a Student's t distribution. Option B is correct. The Jarque-Bera test specifically examines the skewness and kurtosis of the data to determine if they are consistent with a normal distribution. Option C is incorrect because there is no requirement for a Gaussian copula to be applied to the data before conducting the Jarque-Bera test. The test is applied directly to the raw data. Option D is incorrect because the test statistic does depend on the sample size, as indicated by the \( n \) term in the formula. In summary, the correct answer is B: The Jarque-Bera test only takes into account the skewness and kurtosis of a distribution.

Author: LeetQuiz Editorial Team