# Durbin Watson Test Clarity

Okay guys so I get the Durbin Watson Test is used for identifying autocorrelation, and we reject the null if it’s either below the low DW stat or above the high DW stat. But I have something in my notes/memory about accepting/rejecting based on whether DW is greater than, less than or = 2

Can someone clarify these two for me please?

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DW > 2 = negative serial correlation

DW ≈ 2 = no serial correlation

DW < 2 = positive serial correlation

Yea but what if the lower DW critical value is above 2, for e.g. 2.5. Wouldn’t it now be if DW < 2.5 = positive serial correlation?

Those values can be easily remembered by knowing that

DW ≈ 2(1-r)

where r is the correlation coefficient.

DemolitionX wrote:

Yea but what if the lower DW critical value is above 2, for e.g. 2.5. Wouldn’t it now be if DW < 2.5 = positive serial correlation?

I am not entirely sure about the following, so take it with a grain of salt:

From looking at the DW formula a value of 2 indicates (exactly) no autocorrelation of the residuals. Thus a value of D_lower that is greater than 2 is impossible.

It is probably late now, but if 2 = no serial correlation then the closer the values are to 2 regardless of positive or negative serial correlation, you cannot reject. If they are super far away like .16 and 3.99 you are rejecting the null and accepting you have a serial correlation problem. If they fall in between then you are unsure.

I guess for those that read this in prep for next year, I would also ensure you know how serial correlation affects the parameters, consistency of your regression? Are your errors biased? Is the t stat inflated or standard error inflated? What about your F stat? What does negative serial vs positive serial look like on a graph…what are the classics signs of serial correlation. Does it increase chance of type 1 error or type 2 error? how do you correct serial correlation? When can I not use DW stat? I’m sure if you know these concepts, you’ll be fine and positive there are articles on this forum to help synthesis each point above

CA, FRM

Its simple. Forget the business of comparing it to 2. You find the value of 2(1-r). This is your DW test statistic. You then compare it with a critical value. Think of the critical values as 5 sections of a  number line where the number line ranges from 0-4. If the DW statistic falls into the interval:

0 to dL: there is positive serial correlation

dL to dU: test is inconclusive

dU to [4 minus dU]: no serial correlation

[4 minus dU] to [4 minus dL]: test is inconclusive

[4 minus dL] to 4: negative serial correlation

I’m pretty sure the last thing the asker of this question wants to think about now is the Durbin Watson stat!!

sid0496 wrote:
Its simple. Forget the business of comparing it to 2. You find the value of 2(1-r). This is your DW test statistic. You then compare it with a critical value. Think of the critical values as 5 sections of a  number line where the number line ranges from 0-4. If the DW statistic falls into the interval:

0 to dL: there is positive serial correlation

dL to dU: test is inconclusive regarding positive serial correlation, but there is no negative serial correlation

dU to [4 minus dU]: no serial correlation

[4 minus dU] to [4 minus dL]: test is inconclusive regarding negative serial correlation, but there is no positive serial correlation

[4 minus dL] to 4: negative serial correlation

That’s a little better.

Simplify the complicated side; don't complify the simplicated side.

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Yep, yep. Missed out on the detail.

This is how I understood it :

DW = 2 : no serial correlation

DW > 2 : negative serial correlation

DW < 2 : could be positive serial correlation.

In the last case, we need to compare DW with dL and dU, which both are necessarily lower than 2.

If DW < dL : positive serial correlation

Between dL and dU: inconclusive

Between dU and 2 : no positive serial correlation

anasrouetbi wrote:
This is how I understood it :

DW = 2 : no serial correlation

DW > 2 : could be negative serial correlation

DW < 2 : could be positive serial correlation.

In the last case, we need to compare DW with dL and dU, which both are necessarily lower than 2.

If DW < dL : positive serial correlation

Between dL and dU: inconclusive

Between dU and 2 : no positive serial correlation

That’s a little better.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/