>
> You will easily be able to see that that residuals from this
> regression are not independent. So this isn't a counterexample to my
> claim that "There is certainly nothing wrong with using standard
> regression when an explanatory variable is randomly generated, from
> whatever sort of stochastic process you please, as long as the
> regression residuals are independent".
You do not need independent residuals for regression
>
> If you account for this dependence in your test, I don't think you
> will reject the null hypothesis that b=0.
>
Yes you will, if you use standard regression diagnostic.
> >Now the intuition. Consider two time series: 1) US GDP,
> >2) cummulative amount of rain in Brazil. You can think that these series
> >are independent, but try to run 2 on 1 and you will have very
> >significant coefficients.
>
> The two time series may be independent, but if you fit a regression
> model, it will be obvious that the residuals are autocorrelated, and
> you need to adjust for this in doing your significance test.
simple adjustment for autocorrelation won't help
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