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Cooljas · 2022年08月20日

不是说ADF是单尾的吗？那么trend模型里δ0的值是大于critical value的，为啥还会reject H0啊?

  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.



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李坏_品职助教 · 2022年08月20日

嗨，努力学习的PZer你好：


ADF检验的H0是γ=0，H1是γ小于0。

但是ADF检验的统计量主要是看绝对值来判断是否拒绝H0。如果t value的绝对值大于CV（本题中是4.26，明显大于-3.984的绝对值），那就拒绝H0，即认为变量是平稳序列。

这里不需要考虑单尾还是双尾，只看绝对值是否大于CV。



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