Re: Son of unit roots

[ACSLKS@xxxxxxxxxxxxxxxx id <01HMVYQWUWPC8Y6RLT@xxxxxxxxxxxxxxxx>; Fri, 10 Feb 1995 14:39:33 -0400 (EDT)]

> Three questions for the unit root and cointegration crowd:
>
> 1) Is it appropriate to take differences in an I(1) series and compare it
> with an undifferenced I(0) series? For example, share prices are I(1) but
> interest rates, which are regularly cited as a determinant of share value
> (based on theoretical although usually not empirical justifications), are
> I(0). Don't you then have a comparison of differences and levels, and isn't
> this wrong? Moreover, if you take differences on interest rates, haven't you
> then distorted the key attribute of the series (its stationarity) to the
> point of meaninglessness?
>
> 2) In the short-run dynamic equation, provided you have no lagged dependent
> variables on the right side, what qualifies as an "acceptable" r-squared? If
> you're in the range of 0.25-0.35, and all other tests (DW, chi2, maximized
> partial r-squared's, etc.), are acceptable, is it reasonable to stop there?
>
> 3) Is it okay to *delete* from the short-run dynamic equation a variable
> that was used in the long-run static equation?
>
> I expect these questions will sound rather basic to some of you, given the
> level of  discussion I've seen so far. I'm located in Hong Kong and have
> limited access to good textbooks on the subject, however, and would very
> much appreciate your support.
>
> Thanks.
>
>
> JMC in Hong Kong
>

B. Mitchell's response to (2) and (3) need no further comment.  Your question
regarding (1), however, I would like to respond to.  Remember that
cointegration is a necessary condition for the error correction equation to
hold.  If y(t) is I(1) and x(t) is I(0), then x and y are not cointegrated and
you cannot use the error correction representation.  Rule:

          if y(t) is I(1) and x(t) is I(0) then ax(t) + by(t) is I(1)

You can regress differences thru the following model:

          y(t) = b0 + y(t-1) + b1*x(t) + e(t)

Just restrict the coefficient on y(t-1) to one (1) before estimation.


Lonnie K. Stevans
Dept. of BCIS/QM
Hofstra University
Hempstead, NY 11550
USA
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