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st: distribution of DW stat

From   Kit Baum <>
Subject   st: distribution of DW stat
Date   Mon, 22 Nov 2004 19:55:17 -0500

John said

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.

Kit Baum, Boston College Economics

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