In a simple time series regression, say Yt = f (Xt), if presence of either +ve/-ve autocorrelation is found, how could one correct for it "WITHOUT DATA TRANSFORMATION"? Would "Prais-Winsten method with Cochrane-Orcutt transformation" be useful ? Or are there some more useful methods ?
One has to be very careful because autocorrelation of the residuals is not just a problem to be adjusted for but might be a sign of very serious model specification error. So C-O is a way of estimating a model if the error is in the AR form u(t) = pu(t-1) + e(t) where the e is i.i.d. Consider y(t) = bx(t) + u(t) where u(t) is as specificed as above. Substituting for the u(t) gives y(t) = bx(t) + p[y(t-1) - bx(t-1)] + e(t) so if the AR form is 'true' then we have y(t) = bx(t) - pbx(t-1) + py(t-1) + e(t). So AR errors, as has been pointed out by many (including David Hendry) as a special case of y(t) = fx(t) + gx(t-1) + hy(t-1) + e(t) where f.h + g = 0. This should be tested for rather than assume that AR is appropriate.
Hi John, Thanks. The form of AR, whether AR(1) or AR(2) or more could be found out through ACF diagram. But some times, when AR(2) is suggested in in ACF, the regression ut=p1u(t-1)+p2u(t-2) gives insignificant p2 coefficient.... Thats why i was confused.......
Every form of autoregressive error is a general autoregressive distributed lag model with nonlinear restrictions. I usually view bad autocorrelation as a sign of model specification error.
Balaji,
Prais-Winsten or Cochrane-Orcutt methods include Data Transformation procedures. These take into consideration autocorrelation problem if tested for and found to exist.You can first test for model mispecification after your regression and attempt to correct for it.
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