The test statistic vs p-value in ADF test

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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? 

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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