Solved – Durbin-watson test for autocorrelation

Question

Also Durbin Watson test showed to be: Durbin-Watson D=1.672, Number of Obs=171, 1st order autocorrelation=0.162 Do I have autocorrelation problem?

Answer 1

The Durbin-Watson $D$-statistics tests the first order autocorrelation. For a discussion on higher order autocorrelation, see this post.

In order to test for auto-correlation, you need to understand how the test works. The $D$-statistics is obtained as: $D=\Sigma_{t=2}^T(e_t-e_{t-1})^2/\Sigma_{t=1}^Te^2_t$ where $e$ are errors.

This $D$-statistics is bounded by $0$ and $4$, because, in large samples, $D=2-2\hat{\rho}$ where $\hat{\rho}$ is the coefficient in the regression: $e_t=\alpha+\hat{\rho}e_{t-1}+\eta_t$

If $D$ is lower than $2$, then we test positive autocorrelation (a positive residual is followed by a positive residual, in general) whereas we test negative autocorrelation when $D$ is larger than $2$.

The question now, as in every statistical test, is "Is my statistics far enough from my null hypothesis such that I can reject the latter with a certain amount of certainty ?". That is, is the statistics that I obtain beyond the critical value ?

The particularity of the Durbin-Watson test is that you do not have one critical value, but two: a lower bound $D_l$ and an upper bound $D_h$. Since the test is symmetric, you also have the equivalent $4-D_h$ and $4-D_l$.

The test works as follows, if I am between $0$ and $D_l$ or between $4-D_l$ and $4$, then I can reject the null hypothesis of no autocorrelation. If I am between $2$ and $D_h$ or between $2$ and $4-D_h$, then I cannot reject. What happens when I am between $D_l$ and $D_h$ or between $4-D_h$ and $4-D_l$ ? The test cannot conclude on the presence of autocorrelation. It is an indetermination area.

To run the test, you need two things: the number of variables used in your regression and the number of observations. With this, you can find $D_l$ and $D_h$ given in statistical tables like this one. Then you can conclude on the presence of autocorrelation or not.

You do not provide the number of variables used in the estimation, I therefore cannot answer your question, although I have a hunch that it is Ok because of the first order autocorrelation value which is quite low and the value of $D$.