# Durbin Watson

Can someone please explain the upper and lower limits for the Durbin Watson statistic? I can never understand.

without proofing it out…its just the way the DW formula works. If you have perfect negative serial correlation (-1) the DW stat will be 4. If you perfect positive serial correlation the DW stat will be 0.

0 to 4 is the range, anything greater than 2 exhibits negative serial correlation.

If you look at a D-W table, it’ll give you two numbers. They might be, for example, 2.15 and 3.25. This means that if your calculated statistic is less than 2.15, there’s no (negative) serial correlation, and if it’s above 3.25 there is (negative) serial correlation; if it’s between 2.15 and 3.25, there might be, and there might not be; the test is inconclusive.

(For positive serial correlation, the numbers might be, say, 1.2 and 2.7. Above 2.7, no (positive) serial correlation; below 1.2, definite (positive) serial correlation; between 1.2 and 2.7, maybe, maybe not.)

i like to draw out the normal graph and then put in the critical DW values as higher and lower bands. If your testing for negative serial cor then the DW test stat is to the right hand side, if it’s in the middle then in inconclusive, and to the left is no corr.

Just to synthesize it in a way I understand…

Let a = the DW lower bound

Let b= the DW higher bound

Let c = 4 - b

let d = 4 - a

So the #'s from smallest to largest are: 0, a, b, c, d, 4

Zone 1 (0 to a): reject null hypothesis of no positive serial correl.

Zone 2 (a to b): inconclusive about positive serial correlation.

Zone 3, special zone (b to 4, not just b to c): Fail to reject null hypothesis of no positive serial correlation.

Zone 4, special zone( 0 to c): Fail to reject null hypothesis of no negative serial correlation.

Zone 5(c to d): inconclusive about negative serial correlation.

Zone 6 (d to 4): reject null hypothesis of no negative serial correlation.

Is this correct?

Does the schweser book only cover this from the positive correlation perspective? pg. 199-200 If so…shame! lol

Yup.

Is the null always testing for positive serial correlation? Or is it sometimes testing for negative serial correlation.

Why are the upper limits always closer to 2? and lower limits always further away from 2? and Why do you subtract 4- upper or lower limit when DW is above 2? It’s kind of weird because I can’t tell which part of the line I should be looking at and I don’t know how it ties in to 2 (1–r) that Schweser puts in their curriculum.

Sometimes you’re testing for positive and sometimes for negative. The null is “no serial correlation”.

The limits of r are: -1 ≤ r ≤ 1. So 2(1 – r) ranges from 0 (when r = 1) to 4 (when r = -1), and 2(1 – r) = 2 when r = 0. Thus, if the correlation is close to zero, D-W is close to 2; if the correlation is strongly negative (r near -1), D-W is close to 4; if the correlation is strongly positive (r near +1), D-W is close to zero.

Basically just remember that if the DW Stat = 2, you have no serial correlation. If it equals 0, you have negative, and 4=positive. But there isn’t a solid black line where you suddenly go “oh hey, now we’ve got X correlation”. There’s a “grey area”, between the critical DW stats, where the test is inconclusive. There will be two of these ranges on either side of 2, our “safe” value.