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qingcui · 2024年09月18日

选择第三个模型的原因是什么？

  1. FRM I
  2. Quantitative

NO.PZ2020011101000027

问题如下：

ADF tests are conducted on the log of the ten-year US government bond interest rate using data from 1988 until the end of 2017. The results of the ADF with different configurations of the deterministic terms are reported in the table below. The final three columns report the number of lags included in the test as selected using the AIC and the 5% and 1% critical values that are appropriate for the sample size and included deterministic terms. Do interest rates contain a unit root?


选项：

解释：

The first step is to select the appropriate model to use. For these, the statistical significance of the parameters for the constant and trend must be taken into account.

For the trend model, both of these have t-stats with absolute values >4, well within the bounds of statistical significance at even the 99% level. Accordingly, the proper model to study is the last one. For this model, the t-stat on gamma is to the left of the 1% CV—therefore, the null hypothesis of having a unit root is rejected at the 99% confidence level. Note that if the proper model were either the constant or no-trend then the null hypothesis would not be rejected.

老师，我不是很明白为什么要选择第三个模型？能再帮忙解释一下吗，谢谢，盼复！

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1 个答案

pzqa27 · 2024年09月18日

嗨，爱思考的PZer你好：


这个题目考的就是根据stat和critical value的大小，来判断是否拒绝原假设。

我们都把想要拒绝的当做原假设，我们不想要看到unit root，所以原假设H0：存在unit root.

题目给出的表格展示了三个model（none、constant、trend）：

第一个模型none，只有γ一个自变量，括号里的数字代表计算出来的t-stat=-1.666，而在5%和1%significant level下，critical value=-1.942和-2.572，那么计算出来的t-stat落入接受域，接受原假设这个模型存在unit root；

第二个模型constant有γ，δ0两个自变量，同理，两个自变量系数的t-stat也都落入接受域，第二个模型也存在unit root；

第三个模型trend有三个自变量γ，δ0，δ1，这三个自变量系数的stat（图表括号里的数字）均大于CV（critical value），落入拒绝域，拒绝原假设，代表这个模型没有unit root，模型是有效的，选择第三个模型。


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