Durbin-Watson interpretation

[omohojo]

I am getting confused on the two approaches presented related to the Durbin-Watson statistic:

There is the one related to the straight value of the statistic

DW = 2 => No Serial Correlation

DW < 2 => Positive Serial Correlation

DW > 2 => Negative Serial Correlation

AND

There is the other one related to the value of the statistic in relation to critical values

DW < d_l => Reject H₀: positive serial correlation

d_l < DW < d_h => Inconclusive

d_h < DW => Fail to reject H₀: no positive serial correlation

How are these related? It would seem like the first approach would sometimes contradict the second.

I think, in part, I am getting confused because the text sometimes refers to positive serial correlation as simply serial correlation.

[125mph]

I’ve seen both of these interpretations.

My understanding is the 2nd one with d_l and d_h is the precise method, while the first set is a generalization. If DW is is around 2, then you know for sure no serial. If its less than two, then you can say its positive serial. If its a large number, then you know its negative serial correlation.

[letsgo]

For all I know if:

DW is less than the lower critical value -> positive serial correlation

DW is between lower critical value and 4 - lower critical value -> not significant serial correlation

DW is higher than 4 - lower critical value -> negative serial correlation.

and:

if DW = 0 -> max positive serial correlation = 1.

if DW = 2 -> absolute no serial correlation at all.

if DW = 4 -> max negative serial correlation = -1.

[takeo808]

The first interpretation only tells us whether the errors are not serial correlated or serial correlated:

• Not serial correlated if Cov(ε_t, ε_t−1) equals 0; DW will equal 2;
• Serial correlated (if DW ≠ 0)

The second interpretation tests whether the DW stat differs significantly from 2 by showing the value at different levels of serial correlation.

The null hypothesis (no serial correlation) is setup to be rejected if the DW stat is below the critical value (d*). The DW table doesn’t provide the “true” critical value (d*) but provides (d_u) and (d_l) values, giving us a range. If the DW stat is within the range, the test is inconclusive because we don’t know for sure whether it’s above or below the true critical value (d*).