I have a variable named A. Let's name a residual of A = time + c is B. I conducted a root test and found that B is stationary.
In another time, I conducted a root test of A with a setting of "level" and "intercept and trend", I found that A is not stationary.
In my opinion, both root tests should end with the same result i.e stationary
Why did root tests of B and A (level, intercept and trend) result in different results ?
Hi Muhammed:
you conduct 2 tests (a) A is regressed ob time and c then you get the residual (e).
The test then should be: assuming (De= e-e(-1) ), then the new regression should be
De on e(-1) De{-1 ) De(-2) and so on.
The above should yield the same as DA c time A(-1) DA (-1) DA(-2) and so on
Dear Muhammed,
It seems that variable B is simply a detrended form of variable A. I am not very familiar with root tests, but it is clear that, (even) if B is stationary (which is likely for detrended variables), A is not. Maybe that the test for A setting intercept and trend does not really detrend A.
By using these variables you introduced cointegration and series are not stationary.
@ Chuck and all
Just for a double check. I conducted a root test as "level" and "none" for a residual of A = time + c, leading to stationary of a residual of that regression.
But for A itself, I conducted a root test as "level" and "trend and intercept", leading to not stationary of Y. Why these results are different ?
Yes, the second part of the above is a test of "level" so nonstationarity implies possible I(1)
The first part of the above relates to test of stationarity on the residual
@ Chuck,
I repeat your answer,
A root test for the residual is (De= e-e(-1) ), while a root test of "level" and "none" is e(-1) De{-1 ) De(-2)
is that correct ?
As an econometrician, I do not rely on machine generated values so let me explain it:
A root test of the residual is De (no intercept) e(-1) De(-1) De(-2) { put enough De lags to remove serial correlation). Then, look at the t-statistic of e(-1). The null hypothesis is no-cointegration and Ha is cointegration. A large absolute t implies cointegration. because you will reject the null.
A root on level (A) is DA c time A(-1) DA(-1) DA(-2) ---- this is, a test of the null hypothesis of nonstationarity or I(1) and the alternative hypothesis I(0). Here, you want to obtain a small absolute t so that you have nonstationarity.
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