ADF, KPSS and Engle-Granger tests
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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)?
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?
3) While testing cointegration (Engle -Granger test) should I chose version with constant
(or with constant and linear trend)?
Thanks in advance.
Greetings,
Mariusz
Poland
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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
T.: +34 946013732 | F.: +34 946013754
www.et.bs.ehu.es
> 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.
Thanks. But let me ask about something (integration and cointegration are
not 'my topics', so sorry if questions are trivial). What is the role of
deterministic parts in ADF regression? Why we sometimes add constant and
linear trend to ADF regression? It's still I(1) process? Couldn't be better
to test differences of variable with a constant term instead (so second
differences will be dependent variable in ADF regression)?
Greetings,
Mariusz
Poland
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