Course Name: Mean Reversion Strategies In Python, Section No: 3, Unit No: 8, Unit type: Quiz
Answers C and D are not correct since if test does not reach confidence level it proves nothing. Please refresh your stats background.
Correct answer: A
Hi Viktor,
Actually, if the test statistic does not reach the critical level, it proves something. The logic is testing a hypothesis stating something over an alternative hypothesis. In this case, it is non-stationarity. So if the test statistic is lower than the critical value, we reject H0 stating the time series is non-stationarity, and we conclude that the time series is stationary. On the contrary, if the test statistic is higher than the critical value, we do not reject H0 and conclude that the time series is nonstationary.
You can also check this in Gujarati's Basic Econometrics book. In the book, the ADF test is stated as:
"In ADF we still test whether δ = 0 and the ADF test follows the same asymptotic distribution as the DF statistic, so the same critical values can be used."
So we should check for the DF test, and it is stated as:
"All we have to do is to take the first differences of Yt and regress them on Yt−1 and see if the estimated slope coefficient in this regression ( = δˆ) is zero or not. If it is zero, we conclude that Yt is nonstationary. But if it is negative, we conclude that Yt is stationary."
"In each case, the null hypothesis is that δ = 0; that is, there is a unit root—the time series is nonstationary. The alternative hypothesis is that δ is less than zero; that is, the time series is stationary. If the null hypothesis is rejected, it means that Yt is a stationary time series with zero mean…"
In our example, since the test statistic of -2.64 is higher than both critical values (-2.87 for 95%, -3.44 for 99%), we do not reject the null hypothesis. It means that time series is nonstationary for these confidence levels. Therefore, C and D are also correct.
Hope this helps.
Hi Suleyman,
I agree that rejection of H0 tells us something. I am talking about the case when H0 is not rejected, which does not tell us anything, since it may refer both to insufficent data when H0 should be in actuality be rejected as well as the case when H0 is true. The sources you cite refer to the case when we have enough evidence to reject H0 (as they should) and do not support your claim that "we do not reject the null hypothesis. It means that time series is nonstationary for these confidence levels". The latter does not follow from the former. You are making 101 statistics inference mistake claiming that, just like the authors of the question did. You can find disussion of this in any basic course in statistics, see, e.g., Wasserman's "All of statistics": "…we will end up using models where we failed to reject H0. But we might fail to reject H0 due to low power. The result is that we end up with a bad model just due to low power." I hope you can find someone who understands this and will correct answers to the question – otherwise this insistence on statstics inference mistake casts doubts on the quality of materials you provide that are outside of my competence area where I can not identify problems easily.
Hi Viktor,
Yes, you are right, and we will be updating the quiz question and the necessary parts in the course.
Thank you for pointing it out.