2010/1/22 Sven Schreiber <svetosch(a)gmx.net>:
John C Frain schrieb:
> If you include seasonal dummies in the "NO CONSTANT" or "restricted
> constant" it is unlikely that the sum of the seasonals will add to
> zero and you will then be imposing a trend on the undifferenced series
> in the vecm.
Yeah but that's what centered seasonals are for which sum to zero by
construction. We implicitly assumed that Stata's "normalized" s3 easonals
concept means exactly this, because they refer to Johansen's discussion.
So then there wouldn't be any reason to exclude them. But since Stata
doesn't seem to have automatic seasonals, maybe they just don't trust
their users to do it right and play it safe :-)
In Johansen's model 3 with seasonal effects, as far as I can recall,
one includes a constant and 3 seasonal dummies.The fourth seasonal
effect is then the negative of the sum of the 3 seasonal effects that
have been included and the remainder of the constant contributes
towards the unrestricted constant in the equation. If one includes 3
of the seasonals in model 1 or 2 there is no reason why the sum of the
three should be zero. Similarly if 4 are included the method does not
restrict the estimates to add to zero. I think that the main reason
for using centralized seasonals is that they are orthogonal to the
constant. It is nearly 20 years since I wrote programs for Johansen
estimation in Gauss and I have not checked the algebra and may have
forgotten some details.
>
> Stata in the option trend(trend) refers to a quadratic trend in the
> undifferenced data it is correct as this corresponds to a linear trend
> in the differenced data.
But that's not what they say, instead they say:
>>
>> "trend(trend) include a linear trend in the cointegrating
>> equations
My stata manual says the option "trend(trend) is "include a linear
trend in the cointegrating equations and a quadratic trend in the
undifferenced data".
whereas Johansen's/Eviews' option number 5 has a quad trend in the
cointegrating equations (and a linear trend in the differenced data, as
you say).
For other methods the Stata manual and help always seemed to me very
illuminating, but not in this realm. But hey, they're newcomers there...
And in their new version they have decided to include pdf manuals.
Personally I dont like Stata for time series analysis.
-sven
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John C Frain
Economics Department
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.html
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