ADF results

AI & Machine learning
1

Course Name: Financial Time Series Analysis for Trading, Section No: 17, Unit No: 9, Unit type: Notebook

Hello, in this notebook we said if ADF Test Statistic is less than 5% critical value then time series is not stationary.

https://i.imgur.com/NthV722.png

However, in this case ADF Test Statistic is bigger than 5% critical value, so how we can understand this as p-value is 0.29, bigger than 0.05? Is it some kind of mistake?

2

Hi Daniel,



In the notebook it is said that:

  • If the p-value is greater than the critical value (0.05) you fail to reject the null hypothesis and conclude that the time series is not stationary. The p-value is 0.30 which is indeed greater than 0.05, therefore we can conclude that the time-series in not stationary.
  • Alternatively , if the absolute value of ADF test statistics is less than the absolute value of the critical value, you fail to reject the null hypothesis and conclude that the time series is not stationary. The ADF test statistic of -1.98 is indeed less than 0.05 (critical value), therefore again we can conclude that the time-series is not stationary.



    Hope this clarifies your doubt!



    Thanks

    Rushda
3

The ADF test statistic of -1.98 is indeed less than 0.05 (critical value), therefore again we can conclude that the time-series is not stationary.

Sorry, you mean if ADF Test Statistic (-1.98) is less than |-2.89| (absolute value of 5% critical value) is another confirmation of non-stationarity? So we must compared ADF vs Abs. Value %5 critical value, right?

Do you have any source that dive more in deep about ADF and critical value?
4

Yes Daniel, ADF test statistic is another confirmation of non-stationarity.



This might have been confusing in my earlier reply, let me try to simplify:

  • First, with the p-value being greater than the common significance level of 0.05 we can say that the time-series is not stationary
  • Second, the absolute value of the ADF test statistic being less than the absolute value of the critical value further supports the conclusion of non-stationarity.



    And yes, we do have a blog that covers ADF test, you can follow this link to read.



    Hope this helps!



    Thanks

    Rushda
5

ADF Test



Null Hypothesis: Time series is not stationary

Alternate Hypothesis: Time series is stationary



Data points: 

ADF Test Statistic: -1.98
5% Critical Value: -2.89
p-value: 0.30

The p-value associated with the ADF test is 0.30. This p-value indicates the probability of observing the given test statistic if the null hypothesis were true. Since the p-value (0.30) is greater than the commonly used significance level of 0.05, we do not have enough evidence to reject the null hypothesis. And conclude that the time series is not stationary.

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Alternatively, we can compare the test statistics with the critical value.

Since the test statistics (-1.98) is not less or more negative than critical value (-2.89), we do not have enough evidence to reject the null hypothesis and conclude that the time series is not stationary.

I hope this helps.

Thanks