Does anyone know why the Durbin-Watson residual statistic is scaled
from 0 to 4, rather than from perhaps -2 to 2?
Consult any econometrics textbook. Basically the statistic is \sum
(e_it - e_it-1 )/ \sum e_it^2. The variance of the difference (a-b) is
the sum of the variances minus twice the covariance, so if a,b are
independent, the numerator is 2 \sigma^2 and the denominator is sigma^2
-> dw = 2. As \rho->+1, the covariance is a large positive number, and
in the limit cancels out the variance, and dw->0. As \rho -> -1, the
covariance is a large negative number which is similar to the variance,
so the numerator -> 4 \sigma^2 and dw ->4.