Does anybody know the distribution of the residual mean square when a linear regression model is fitted with autocorrelated AR(1) errors (e.g. using PROC AUTOREG in SAS)? I suspect that it is probably chi-squared with reduced d.f. but cannot find the formula for the d.f.
The reason for the question is that I am trying to compare variations in daily figures (which vary linearly with time) before and after an intervention. I will do this by comparing the "before" and "after" RMS's using an F-test, but I need to know the correct d.f. to use.
Please note that I am interested in the distribution of the RMS as measured about the fitted regression line
y(t) = a + b.t + e(t)
i.e.
RMS = sum (yobs - yfitted)**2 / (n-2)
rather than the variance of the innovations a(t) in the AR(1) error model
e(t) = rho.e(t-1) + a(t)
|