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syfzln · 2025年03月23日

峰度

NO.PZ2023091601000025

问题如下:

In looking at the frequency distribution of weekly crude oil price changes between 1984 and 2008, an analyst notices that the frequency distribution has a surprisingly large number of observations for extremely large positive price changes and a smaller number, but still a surprising one of observations for extremely large negative price changes. The analyst provides you with the following statistical measures. Which measures would help you identify these characteristics of the frequency distribution?

I.Serial correlation of weekly price chances

II.Variance of weekly price changes

III.Skewness of weekly price changes

IV.Kurtosis of weekly price changes

选项:

A.

I, II, III and IV

B.

II only

C.

III and IV only

D.

I, III and IV only

解释:

The question considers a skewed leptokurtic distribution. To measure the magnitude of these skewed tails, the analyst needs to consider both the skewness and kurtosis

这题说右极端值很多,可以判断出右偏,峰度是怎么判断的?如果想要知道峰度(比如两端肥尾的情况),就不能判断出向哪偏了吧?

1 个答案

李坏_品职助教 · 2025年03月23日

嗨,从没放弃的小努力你好:


题目说的是,large positive price changes以及 large negative price changes出现的频率都是惊人的,说明左右两个尾部的数据都比正态分布要多,那说明是肥尾特征。一般情况下肥尾对应尖峰,此时kurtosis是比正态分布更大的。


而且题目也说了negative change的数量是“smaller number”,意思是右尾的极端值比左尾更多,那说明数据是右偏的。正态分布是0偏度,所以也和正态分布不一样。


所以这道题的信息可以判断出skew以及kurtosis这两个指标的特征。

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