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· 2022年01月23日

a选项依然存疑

NO.PZ2016062402000052

问题如下:

Which of the following four statements on models for estimating volatility is incorrect ?

选项:

A.

In the EWMA model, some positive weight is assigned to the long-run average variance rate.

B.

In the EWMA model, the weights assigned to observations decrease exponentially as the observations become older.

C.

In the GARCH(1,1) model, a positive weight is estimated for the long- run average variance rate.

D.

In the GARCH(1,1) model, the weights estimated for observations decrease exponentially as the observations become older.

解释:

The GARCH model has a finite unconditional variance, so statement c. is correct. In contrast, because α1+β\alpha_1+\beta sum to 1, the EWMA model has undefined long-run average variance. In both models weights decline exponentially with time.

看到之前的解答中有提到,a是只为正数,而c是可以为正数。我想问的是,难道weighted不是只能为正数吗?为什么选项a还是错误呢,烦请解答一下,谢谢~

1 个答案

李坏_品职助教 · 2022年01月23日

嗨,从没放弃的小努力你好:


A说的是EWMA模型里面,有一部分正的权重被分给了长期volatility。但是EWMA实际上是GARCH模型的特殊形式,EWMA里面对长期波动率的参数是0.所以A是错误的。


在EWMA的模型里面(讲义P324),是没有长期波动率的:



而GARCH模型如下:


所以GARCH里面的w这一项,在EWMA里面被剔除了。


C说的是garch(1,1)模型中,给长期平均方差V预估了一个正的权重,就是γ参数大于0,是正确的。


这道题选错误的选项,所以选A.


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虽然现在很辛苦,但努力过的感觉真的很好,加油!