- If both series have a unit root and are NOT cointegrated, can we use linear regression? 2. If both series have a unit root and are cointegrated, can we use linear regression?
I may have this reversed but: 1) No 2) Yes
Were you reading this in the CFAI text? I think the author of that section was not sure what the answer to this was and intentionally obfuscated the explanation. I really doubt that you’ll see any question of this sort on the test but I’ll try to find a moment to explain in a bit.
the answer is definitely: 1) No 2) Yes
Exactly. If 2 times series have a unit root and are both cointegrated, use the regression. If one has a unit root and the other does not, you cannot use the regression. I believe you correct with DF-EG t test stats? (anyone?) But, seriously, you think THAT will be on the test? That’s like asking you to distinguish between a random walk and a random walk with drift (the only difference here is that in the latter b0 is >0).
it was on the sample test
I’m no econometrician, but perhaps this will help… ::takes deep breath:: If a series has a unit root, it is not covariance stationary (CovStat). It might be, say, a random walk. Nonetheless, there may be a linear relationship between two such series. Cointegration, if present, says that there is a statistically significant linear relationship – more specifically a correlation – between the two series and that linear regression is appropriate… In more detail, remember that we can only use our normal regressions with a fair amount of confidence/success on CovStat time series. Fortunately we can sometimes convert non-CovStat time series into CovStat time series by “differencing”. Also, remember we can difference multiple times, so we can “first difference” or “second difference” a time series. OK, so what does cointegration mean? Well actually what does integration mean in the time series sense? It’s the opposite of differencing, where “first differencing” is when we take the delta of a time series rather than the time series itself, is a discrete derivative. What’s the opposite of derivation…? Integration. Taking some technical liberties, it is reasonable to say that the Engle-Granger test of cointegration says the time-series both “achieve” CovStat when “differenced” the same number of times, AND there is a linear relationship between the two series. So, cointegration is a special case where you CAN use linear regression, even though you could not use it on the underlying series themselves.
justin88 Wrote: ------------------------------------------------------- > I’m no econometrician, but perhaps this will > help… ::takes deep breath:: > > If a series has a unit root, it is not covariance > stationary (CovStat). It might be, say, a random > walk. Nonetheless, there may be a linear > relationship between two such series. > Cointegration, if present, says that there is a > statistically significant linear relationship – > more specifically a correlation – between the two > series and that linear regression is > appropriate… > > In more detail, remember that we can only use our > normal regressions with a fair amount of > confidence/success on CovStat time series. > Fortunately we can sometimes convert non-CovStat > time series into CovStat time series by > “differencing”. Also, remember we can difference > multiple times, so we can “first difference” or > “second difference” a time series. > > OK, so what does cointegration mean? Well > actually what does integration mean in the time > series sense? It’s the opposite of differencing, > where “first differencing” is when we take the > delta of a time series rather than the time series > itself, is a discrete derivative. What’s the > opposite of derivation…? Integration. > > Taking some technical liberties, it is reasonable > to say that the Engle-Granger test of > cointegration says the time-series both “achieve” > CovStat when “differenced” the same number of > times, AND there is a linear relationship between > the two series. > > So, cointegration is a special case where you CAN > use linear regression, even though you could not > use it on the underlying series themselves. Trying to show off there, Justin? I kid.
Damil4real Wrote: ------------------------------------------------------- > Trying to show off there, Justin? > > I kid. What?? You cannot reject the null hypothesis that I am not trying to show off. 
In all seriousness, I had the same exact question while reading the CFAI text for that very section last night. I ended up spending an hour or so researching the topic on my own so I thought I’d brag… errrr… try to be helpful.
In schweser video, instructor gives a nice example on this. Hard to forget! It was something like this: 1. If both person in a marriage are sane, marriage will last. 2. If one is sane and the other is insane, marriage will not last. 3. If both are insane, but insane in same way (both think day is night and night is day), their marriage will last. 4. If both are insane, but insane in different ways, their marriage will not last. Now, whether it comes in exam or not, i am going to remember it for a long time
that is an excellent explanation