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亚利 · 2023年05月20日

这题想问什么

  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?


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.

这题想问的是什么，问题是问有没有单位根，答案落在模型选择上是为什么。constant and trend 和none跟利率是什么关系，跟单位跟什么关系？

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2 个答案

品职答疑小助手雍 · 2023年05月22日

ADF检验也有增加deterministic项和用不同lag试错的过程，所以就假设了三个模型看哪个有效，验证单位根的过程也是找到正确模型的过程。

最后相当于找到了合适的模型，其差分和趋势项可以使模型没有单位根的问题。

品职答疑小助手雍 · 2023年05月21日

同学你好，题目给出的表格展示了三个model（none、constant、trend）

因为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.

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。

使用trend这个模型， 又因为检验单位根用的γ的t检验也是显著不等于0的，所以它没有单位根。

亚利 · 2023年05月21日

老师您回答的这些我明白的，但是您没有回答我的问题，“”这题想问的是什么，问题是问有没有单位根，答案落在模型选择上是为什么。constant and trend 和none三个模型跟利率是什么关系，跟单位跟什么关系？”

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