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Kathy苏苏 · 2023年05月25日

请翻译并详解B和C选项,谢谢老师!

NO.PZ2016070202000007

问题如下:

Extreme value theory (EVT) provides valuable insight about the tails of return distributions. Which of the following statements about EVT and its applications is incorrect?

选项:

A.

The peaks over threshold (POT) approach requires the selection of a reasonable threshold, which then determines the number of observed exceedances; the threshold must be sufficiently high to apply the theory, but sufficiently low so that the number of observed exceedances is a reliable estimate.

B.

EVT highlights that distributions justified by the central limit theorem (e.g., normal) can be used for extreme value estimation.

C.

EVT estimates are subject to considerable model risk, and EVT results are often very sensitive to the precise assumptions made.

D.

Because observed data in the tails of distribution is limited, EV estimates can be very sensitive to small sample effects and other biases.

解释:

EVT estimates are subject to estimation risk, so statement c. and d. are correct. However, EVT does not apply the central limit theorem (CLT), which states that the average (as opposed to the tail) of i.i.d. random variables is normal.

请翻译并详解B和C选项,谢谢老师!

1 个答案

pzqa27 · 2023年05月25日

嗨,努力学习的PZer你好:


B选项说:EVT强调,由中心极限定理证明的分布(如正态)可用于极值估计。

这个是不对的EVT是研究极端值的情况的,中心极限定理并不适用于极值

C选项说:EVT估计受制于相当大的模型风险,而且EVT结果往往对所做的精确假设非常敏感。

这个是对的,因为极值理论是对高于门槛值的尾部进行建模研究的,所以它肯定非常异常门槛值的选择。而且极值理论中的分布函数也很复杂,对一些误差就会较为敏感了。

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