"Radford Neal" <[EMAIL PROTECTED]> a écrit dans le message news:
> >If the explanatory variable is generated by an integrated process, it
won't
> >work, even if the error term is an iid process.
>
> This is what I am disputing. What basis do you have for claiming that
> it won't work? And in what sense do you mean that "it won't work"?
>
> I suspect that you've encountered a claim that is somewhat like this
> in some reference book, and have mis-interpreted it.
>
> Radford Neal
>
Well, I may have not explained myself very clearly, or understood what you
really meant, in which case I apologize in advance.
Now, here is what I mean when I say that standard procedures shouldn't work
with integrated processes.
If X is non stationary, and if the regression equation is true, Y is non
stationary too.
The OLS slope estimator is (X'X)(-1) X'Y
If the X is generated by an integrated process, (X'X) will not be convergent
in probability, nor will X'Y.
In the case of Y and X being two independent random walks, the mean of
(XX)(-1)X'Y can be calculated using Wiener distribution theory however, and
it is not zero (it looks very bad). The t-stat for slope is not zero either.
The variance of both slope estimator and t-stats are much higher than
standard theory forecast, and, what is even worse, do not decrease as sample
size increase.
David B
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