I think the original article on this subject is Granger and Newbold (1974) Journal of Econometrics. Greene's Econometric Analysis has a discussion, the gist of which is that two independent random walks will appear to be spuriously correlated in a regression. -Dick Startz
On 23 Oct 2001 22:12:33 GMT, [EMAIL PROTECTED] (Radford Neal) wrote: >In article <9r4nbg$dka$[EMAIL PROTECTED]>, >David B <[EMAIL PROTECTED]> wrote: > >>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. > >That's true, but why is it a problem? Since X is non-stationary, you will >get data over a larger and larger range as time increases. Having data over >a large range is GOOD. It lets you pin down the regression coefficients >more easily. > >>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. > >If Y = a + b*X + i.i.d. noise, X and Y can't be independent random walks. >If the noise is not independent, then you need to account for that when >computing the standard error. > > 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 >---------------------------------------------------------------------------- ---------------------- Richard Startz [EMAIL PROTECTED] Lundberg Startz Associates ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
