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Othor · 2023年02月14日

麻烦讲解一下I和III,谢谢!

NO.PZ2018122701000058

问题如下:

Which of the following statements about correlation and copula are correct?

I.Copula enables the structures of correlation between variables to be calculated separately from their marginal distributions.

II.Transformation of variables does not change their correlation structure.

III.Correlation can be a useful measure of the relationship between variables drawn from a distribution without a defined variance.

IV.Correlation s a good measure of dependence when the measured variables are distributed as multivariate elliptical.

选项:

A.

I and IV only

B.

II, III, and IV only

C.

I and III only

D.

II and IV only

解释:

A is correct.

考点 Copula Functions

解析

"I" is true. Using the copula approach, we can calculate the structures of correlation between variables separately from the marginal distributions. "IV" is also true. Correlation is a good measure of dependence when the measured variables are distributed as multivariate elliptical.

"II" is false. The correlation between transformed variables will not always be the same as the correlation between those same variables before transformation. Data transformation can sometimes alter the correlation estimate. "III" is also false. Correlation is not defined unless variances are finite.

I和III不是很明白,

ICopula enables the structures of correlation between variables to be calculated separately from their marginal distributions.是翻译成“Copula根据变量的边缘分布分别计算变量之间的相关性的结构”吗?这个具体的逻辑没太明白,变量的边缘分布,是指高斯copula中的G1(u1)吗

III.Correlation can be a useful measure of the relationship between variables drawn from a distribution without a defined variance.

这里的drawn from a distribution without a defined variance.请问指的是什么?

谢谢!

2 个答案

DD仔_品职助教 · 2023年02月15日

嗨,从没放弃的小努力你好:


1,marginal distribution叫做边际分布,是公式里的u1,u2,u3, ... ,一直到un

2,draw from的意思是提取,without a defined variance的意思是没有一个定义的方差,直接翻译就是:从一个没有定义方差的分布中提取。

用白话就是:我们连这个分布的方差是啥都不知道。既然方差是啥都不知道,就没办法求相关系数,相关系数对于这个分布就不是一个有用的衡量标准。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

DD仔_品职助教 · 2023年02月14日

嗨,从没放弃的小努力你好:


同学你好,


I的意思是copula 可以根据每个变量的marginal distribution(概率密度函数)去计算他们的相关系数structure。比如Gaussian copula就是利用标准正态分布去计算相关系数的结构。


III说的是如果我们没有俩个变量的方差信息的话,我们也可以计算相关系数,这话不对。相关系数=协方差除各个资产的方差,连方差都不知道根本就没办法求相关系数,那么相关系数就没啥用了。或者在方差无限大的情况下,相关系数页无法得出。

.



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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

Othor · 2023年02月15日

请问marginal distribution对应copula公式里的什么?drawn from a distribution without a defined variance怎么翻译?

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