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 ---------------------------------------------------------------------------- ================================================================= Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =================================================================
