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柚柚_柚 · 2020年05月31日

问一道题:NO.PZ2020011101000027 [ FRM I ]

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.

先选择合适的模型,因为只有trend model的系数和常数项通过了t检验(显著不等于0),所以使用这个模型。 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。(我的问题 是为什么显著不等于零所以每单位根 最后一句话是说如果选择了前两个模型,那有单位根的原假设不会被拒绝。
2 个答案
已采纳答案

小刘_品职助教 · 2020年05月31日

同学你好:

1)因为原假设是有单位根,而γ的t检验结果是小于1% critical value的,所以拒绝原假设;

2)第二句话是如果选了前两个模型,因为γ的t检验结果都是大于对应的1% critical value,所以不能拒绝原假设。

可以看一下原版书的以下标绿色的内容:

小刘_品职助教 · 2020年06月02日

同学你好,

你可以看一下11.3那边的话,sigma0 代表的是常数项,sigma1代表的是系数。

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