It won't work in the following sense. Suppose that you run a regression of y on x trying to estimate a relationship of the form y=a+bx+u. Further suppose that y(t)=y(t-1)+e1(t) and x(t)=x(t-1)+e2(t), so both processes are integrated. Further, suppose that e1 and e2 are independent and thus there is no relationship between y and x. you have estimated your coefficient b and trying to test that b=0. Now the main part: you will discover that coefficient value is very small but t-statistic is very large imposing that b is not zero. The problem with integrated regressors is that t-statistic diverges to infinity as sample size increases when y and x are independent. Further, in the case of integrated regressors and dependent variables the asymptotic distribution of coefficients is no longer normal.
So, "won't work" means that you cannot test the relationship between variables using standard tools (F tests) when you have integrated variables. 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. Now, what to read. you can try any modern textbook on time series. My recommendation White "Asymptotic Theory for Econometricians" or Davidson "Econometric Theory" On 23 Oct 2001, Radford Neal wrote: > In article <9r4ao0$l07$[EMAIL PROTECTED]>, > David B <[EMAIL PROTECTED]> wrote: > >> 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 > > > >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 > > ---------------------------------------------------------------------------- > Radford M. Neal [EMAIL PROTECTED] > Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED] > University of Toronto http://www.cs.utoronto.ca/~radford > ---------------------------------------------------------------------------- > ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
