In article <[EMAIL PROTECTED]>, Vadim and Oxana Marmer <[EMAIL PROTECTED]> wrote:
>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. 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". If you account for this dependence in your test, I don't think you will reject the null hypothesis that b=0. >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. 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/ =================================================================
