0
$\begingroup$

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?

$\endgroup$

1 Answer 1

2
$\begingroup$

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 $D$.

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.