[Gretl-users] ADF, KPSS and Engle-Granger tests

[Ignacio Diaz-Emparanza]

El Thursday 27 March 2008 11:38:51 Mariusz Doszyń escribió:
> Dear gretl users,
> Given variable y follows a quadratic trend.
> 1) In ADF test should be chosen variant with constant and linear trend and
> this test should be made for the levels of variable (not differences)?

No. If you think, I suppose based on the graphic, that your series follows a 
quadratic trend, it is very probably your series really be I(2). In that case
the ols estimators of the ADF equation in levels are inconsistent, and the 
t-statistic does not follow the DF distribution. You should start with the 
series in differences (+ linear trend), so testing first the second unit 
root.

> 2) 
> I'd like to confirm results obtained from ADF test by doing KPSS test. KPSS
> test should be made for first differences with chosing linear trend?

Yes. Under H_0 you will have an at most I(1) series, under H_a the series will 
be I(2).

> 3) 
> While testing cointegration (Engle -Granger test) should I chose version
> with constant (or with constant and linear trend)? Thanks in advance.

The deterministic part of the cointegration equation is not directly related 
to the deterministic part of the variables. I suggest to start with the more 
general model.


-- 
Ignacio Diaz-Emparanza  
DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA)                                        
UPV/EHU
Avda. Lehendakari Aguirre, 83 | 48015 BILBAO
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