The test statistic vs p-value in ADF test

Course Name: EPAT, Section No: 6, Unit No: 9, Unit type: WaterMarkVideo

I recently conducted an ADF test on a time series, and I am seeking your guidance in interpreting the results.

Here are the specific values from the ADF:

Test Statistic: -2.70 p-value: 0.072

Which of these values should I focus on to draw conclusions about the stationarity of the time series? 

Hi Animesh,



When interpreting the results of an ADF test, we need to focus both on the test statistic and the p-value. These values provide information about the stationarity of the time series.


  1. Test Statistic: In your case, the test statistic is -2.70. This value represents the strength of the evidence against the null hypothesis of non-stationarity. A more negative (i.e., lower) test statistic generally indicates stronger evidence in favour of stationarity. Thus, a test statistic of -2.70 suggests some evidence in favor of stationarity, but the magnitude of the statistic alone is not sufficient to draw definitive conclusions.


  2. P-value: The p-value associated with the ADF test indicates the probability of observing a test statistic as extreme as, or more extreme than, the one obtained under the null hypothesis of non-stationarity. In your case, the p-value is 0.072. Typically, a significance level is chosen (e.g., 0.05 or 0.01). If the p-value is smaller than the chosen alpha, we reject the null hypothesis in favor of stationarity. Conversely, if the p-value is more significant than the chosen alpha, we fail to reject the null hypothesis, suggesting evidence of non-stationarity. In your case, with a p-value of 0.072, it is larger than 0.05 (assuming a common significance level of 0.05), which suggests that you do not have sufficient evidence to reject the null hypothesis of non-stationarity. However, the p-value is relatively close to 0.05, so you may want to consider the context and other factors when making a decision.



    So basically, the test statistic and p-value provide complementary information for interpreting the results of an ADF test. While the test statistic indicates the strength of evidence in favor of stationarity, the p-value helps determine the statistical significance of the test. 



    Hope this helps!



    Thanks,

    Akshay