Stationarity

[Studentka]

I am doing some time-series econometrics analysis and stumbled upon an interesting fact...

DF-GLS test for stationarity indicates that my variable is stationary in levels but non-stationary in first differences.

Being new to this matter, I was wondering how that could be possibly rationalized?

Thanks!

 

[Ken Abbott]

What time series? I can't think of how this can be.

 

[quantie]

I have to admit I don't get it either. Sorry. Something seems to be off.

 

[Polter]

Well, if you take a stationary I(0) process and you (over-)difference, you obtain an anti-persistent I(-1) process.

Don't have Elliot, Rothenberg & Stock (1996) handy, but http://www2.econ.iastate.edu/classes/econ674/falk/lecture_25_ur_tests_III.doc and http://www2.dse.unibo.it/golinelli/teaching/phd/Lecture suggest DF-GLS has been designed to test
H0: Yt ~ I(1), no drift
against
HA: Yt ~ I(0), no restriction on the mean.

-1 is not equal to 0 (or 1), so it's probably not a good idea to use this test for an anti-persistent I(-1) process.

In general, what you observe is perhaps an artifact of over-differencing; look for this (and "overdifferencing" -- spelling varies) term in the following:
http://books.google.com/books?id=fHncWAbCt3MC&pg=PA13
http://economia.unipv.it/pagp/pagine_personali/erossi/rossi_unit_roots_PhD.pdf
http://www.richmondfed.org/publications/research/economic_quarterly/1993/spring/pdf/mccallum.pdf
http://www.duke.edu/~rnau/411arim2.htm

For more on anti-persistence, see:
http://www.stat.cmu.edu/~gmg/home/index.php?option=com_rubberdoc&view=doc&id=5&format=raw // See Remark 2.1.2
http://webpages.lss.supelec.fr/perso/bondon_pascal/509.pdf