ADF lag length selection and normality of residuals?
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Hello,
I'm doing some work with unit roots and cointegration applied to energy
prices. Currently I've run into a bit of a dilemma regarding the choice of
lag length for the Augmented Dickey Fuller tests for stationarity. The
problem is, that for one of the tested variables, I don't get normal
residuals regardless of how many lags I include in the ADF regression. Does
anyone have any suggestions on how i should tackle this?
Best regards,
Olle Olsson, Uppsala, Sweden
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On Mon, 6 Oct 2008, Olle Olsson wrote:
Hello,
I'm doing some work with unit roots and cointegration applied to energy
prices. Currently I've run into a bit of a dilemma regarding the choice
of lag length for the Augmented Dickey Fuller tests for stationarity.
The problem is, that for one of the tested variables, I don't get normal
residuals regardless of how many lags I include in the ADF regression.
Does anyone have any suggestions on how i should tackle this?
As far as I know, normality is not needed at all for the validity of the
asymptotics of the ADF test. Ignacio, can you confirm this?
A personal opinion: I think that the importance of normality tests as
linear regression diagnostics is _highly_ overrated among practitioners.
None of the asymptotic properties of OLS depend in any way on normality.
In small samples, it's another matter, but then, all normality tests I can
think of are asymptotic anyway. The normality assumption is crucial (and
can be tested) in models like probit or heckit, but definitely not OLS or
ADF.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
El Tuesday 07 October 2008 18:52:52 Riccardo (Jack) Lucchetti escribió:
On Mon, 6 Oct 2008, Olle Olsson wrote:
> Hello,
>
> I'm doing some work with unit roots and cointegration applied to energy
> prices. Currently I've run into a bit of a dilemma regarding the choice
> of lag length for the Augmented Dickey Fuller tests for stationarity.
> The problem is, that for one of the tested variables, I don't get normal
> residuals regardless of how many lags I include in the ADF regression.
> Does anyone have any suggestions on how i should tackle this?
As far as I know, normality is not needed at all for the validity of the
asymptotics of the ADF test. Ignacio, can you confirm this?
Yes, the ADF test only needs iid errors.
Probably Olle Olsson is more worried about autocorrelation of residuals.
The ADF regression is based in a AR representation, if your series is better
modelled as a MA probably you will need a lot of AR lags to fit correctly
your series. How many observations do you have, Olle?
--
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
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Ignacio Diaz-Emparanza -
Olle Olsson -
Riccardo (Jack) Lucchetti