>
> In any case, the original poster explicitly claimed that regression
> with an explanatory variable that was generated by a non-stationary
> process was invalid even if the residuals of the regression are
> independent. I claim that this is not true.
if both dependent and independent variables are I(1), residuals are
iid then you have cointegration. Standard tools (Wald , Likelihoo
ration and Score tests ) are
invalid because limiting distribution of estimators is not Normal.
Anyway, to use these standard tools some moment conditions on variables
appearing in regression have to be satisfied. For example, sup E(Xt^2) has
to
be finite which is not true if Xt is integrated.
>
>
> Coefficients:
> Estimate Std. Error t value Pr(>|t|)
> (Intercept) 15.51024 0.62466 24.83 <2e-16 ***
> x 0.40863 0.01898 21.52 <2e-16 ***
> ---
> Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
>
it speaks for itself: how often do you see t-stat=22? Actually, I would
recommend you to repeat this experiment for example 100 times and to check
how many time you cannot reject b=0.
> adjusting for autocorrelation you will conclude that you effectively
> have about five data points' worth of information. I don't think you
> will reject the null hypothesis.
the only adjustment that is going to work here is to difference the data.
>
>
>
> Why are you interested in E(inv(X'X)X'Y)? I think you may be trying
> to find standard errors by finding the unconditional variance of the
> estimators. You shouldn't do this, however. You should be finding
> the variance conditional on the observed X, since X in itself is not
> informative regarding the regression coefficients.
That's right, if you can condition on X and E(U|X)=0 then it's not very
different from fixed regressors ccase. But
sometimes you cannot condition on X (in time series models). Also,
sometimes you cannot or do not want to assume that E(U|X)=0. So, there are
cases when you have to deal with unconditional moments.
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