Dear all:
Few weeks ago I put two messages relative to the differences in p-values in
ADF test in different some packages. The message suumarized was like this:
"By comparing the results with Eviews or R (package fUnitRoot) I get the
same t-statistic, but although all programs indicate that the critical
values are McKinnon (1996) MacKinnon, J. G. (1996) "Numerical
distribution functions for unit root and cointegration tests", Journal of
Applied Econometrics 11: 601-618 p-values of the test are very different
in either case .
Gretl: t = -3.62 p-value 0.02 asymptotic
Eviews t = -3.62 p-value (one-sided) = 0.04 which is the same value
obtained in R.
But investigating a more litle, I have found that the difference is due
that Gretl uses the asymptotic critical value of MacKinnon (1996) and
Eviews and fUnitRoots R-Package gives the critical value of response
surface for finite samples. However, the article of MacKinnon (1996)
suggests (if I understand correctly), that the values computed for finite
sample, it should only be used only in the DF test and not for ADF
augmented as is done in Eviews or fUnitRoots. Is this correct?."
>From Eviews team I have received this answer:
"Your reading of MacKinnon's comment about finite sample ADF values is
generally correct, though there is no evidence presented that they are
better or worse than the asymptotic values for the t-stat. I will point out
that the one case (z-stat) where MacKinnon strongly cautions against using
the finite sample values is not a test statistic that EVIews produces for
the ADF (though we do report related tests in the cointegration context --
perhaps in this case we shouldn't...). I think that the jury is still out
on whether the t-statistic finite sample or asymptotic values are better.
To provide some context, the basic idea is that that the finite sample
critical values are based on a set of simulations for which MacKinnon did
not employ ADF regressions. Were he to have run some with ADF corrections
he might very well have found that the finite sample DF results were closer
than the asymptotic results in some cases (but understandably he did not
run those simulations as the number of simulations that he did run is
already quite large and it is not clear the best way to set up the
correlation structure for evaluating the test statistics).
The most compelling argument for continuing to use the finite sample values
for the ADF is, I think, one of comparability. One concern with switching
over to the asymptotic values for ADF tests is that if you were to run a DF
test for a smallish sample and then add a single ADF lag, you are more
likely to get quite different results if we were to switch to using the
asymptotic values--and in the absence of simulation results it is not clear
whether this is a good or a bad thing. It would then be difficult to
evaluate whether the difference in results is the result of the
autocorrelation correction or the result of different critical values (or
both). With either the finite sample or asymptotic choice, one is in a bit
of a bind in the absence of finite sample simulations. By sticking with the
finite sample values we are at least holding one thing somewhat
constant...this may or may not be better...
As I write this, it occurs to me that one possibility would be to report
both values. That has it's own set of issues but would then allow users to
pick what they want to evaluate. I'll put it on a list of things to
consider."
Some authors from fUnitRoot, urca package or other people using R can
explain me his point of view?
Is curiosity.
Thanks in advance and sorry for any inconvenience.
José F. Perles
University of Alicante
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