Questions on Time Series

CFA Level II Quant
#1

I have two quick questions, both are from Schweser reading 13.

Q18: It’s said that a random walk cannot be fit as an AR(1) model. I thought you can still use AR(1) to model a random walk. It’s just that the AR process won’t be stationary, no?

Q19: Dickey-Fuller unit root test: if the test statistic is significant, we reject the null hypothesis of a unit root, which means that the process is stationary, right? So statement C is not correct. Why is C not the answer (since it asks for the incorrect statement).

Thanks in advance guys.

#2

You can’t go from a RW to an AR(1) directly. You can attempt to correct a RW by first differencing the time series. If the series has a seasonal component, then including a seasonal lag may help. At this point, if the series is stationary, THEN go to an AR(1) model.

You’d get quicker responses if you include complete questions/choices in your posts. I don’t know what option C is. Regardless, in the DF test, the null is, H0: the series has unit root and is nonstationary. So if you reject null, the series may be stationary. If the option in Schweser says otherwise, Schweser probably has a mistake in its material. Frankly, this won’t be surprising since their material is wrong elsewhere. A couple of QBank questions I solved claimed equations like y = x^3 are not linear. Based on my background in stats and the CFAI material, this is blatantly wrong.

Sorry for the digression, but had to put it out there. Just venting coz am pissed about the differences between IFRS and GAAP in FRA.

#3

Sorry, should have included the question and answer options.

Q: Which of the following is not correct about the Dickey-Fuller unit root test for nonstationarity?

A. The null hypothesis is that the time series has a unit root.

B. A hypothesis test is conducted using critical values computed by Dickey and Fuller in place of conventional t-test values.

C. If the test statistic is significant, we conclude that the time series is nonstationary.

I get why A is the answer here but why isn’t C?

#4
#5

H0: Time series has unit root and is nonstationary.

If the test stat is significant, you reject the null. If you reject the null, the series is stationary. So C can’t be the answer.

As a side note, the null in the DF test is exception to the norm - nulls for heteroskadisticity and serial correlation are “no heteroskadasticity” and “no serial correlation,” respectively. The DF null is more in line with the regular t-test null. That is, the nulls for DF and t-tests indicate things we want to reject. Whereas nulls for heteroskadisticity and serial correlation indicate things we want to accept.

Hope this helps.

#6

Exactly what I thought. You reject the null, the series is stationary so C is incorrect hence should be the answer since it is asking for the incorrect statement, no? Or am I missing something here?

#7

Sorry, missed the “not correct” part. C is right. You should check against the Schweser errata, but even if they don’t have it in there, you’re right.

BTW, why do you think A is also the answer? Maybe because it is missing the “nonstationary” portion, but that would really make this question weird. Which won’t be surprising since I have seen Schweser give wrong answers/explanations elsewhere.