NO.PZ2024030508000081
问题如下：
A senior analyst is presenting to a group of newly hired junior analysts on the concepts of coskewness and cokurtosis and how they apply to pairs of random variables. The analyst also compares these measures to general skewness and kurtosis. Which of the following statements about coskewness would the senior analyst be correct to make?
选项：
A.The coskewness of two variables is unit-free, but is not scale-free.
B.The calculation of coskewness requires the cube of the standard deviation of one variable.
C.Coskewness specifically estimates the strength of the dependence of one variable on the signed extreme values of the other variable.
D.When the direction of one variable is insensitive to the magnitude of the other variable, the coskewness measures are zero.
解释：
Explanation: D is correct. When there is no sensitivity on the part of the direction of one variable to the magnitude of the other, this means that the two coskewnesses are 0.
A is incorrect. The coskewness is standardized and is therefore both unit-free and scale-free.
B is incorrect. For the standardization of the cross-third moment, coskewness requires the variance of one variable and the standard deviation of the other. The cube of the standard deviation of both variables is required only by cokurtosis.
C is incorrect. This refers to cokurtosis, particularly the non-symmetric cokurtosis configurations which capture the agreement of the variable signs when the magnitude is large. That is, they measure the strength of the dependence in the signed extremes.
Learning Objective: Explain how coskewness and cokurtosis are related to skewness and kurtosis.
Reference: Global Association of Risk Professionals. Quantitative Analysis. New York, NY: Pearson, 2023, Chapter 5, Sample Moments [QA-5].
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