On Topic Test Dennehy we are given the below:
Durbin-Watson Statistic: 1.89
Durbin-Watson critical values (5% significance)
1.63
1.72
What do 1.63 and 1.72 signifiy? dl & du?
Reject (+) Reject (-)
0--------------dl------(du)-----------(4-du)--------(4-l)-------------4
Reject null if between 0 and dl, and reject between 4-l and 4. Since we only reject if below dl or above 4-dl why do we even need du? I got the answer right since it was clearly above the critical values but I understood this memorizing dl & du and instead they just gave us numbers.
Because between (dl) and (du), as well as between (4-du) and (4-dl), the test is inconclusive, while in the “middle”, between (du) and (4-du) we fail to reject the null, i.e. there is no (positive or negative) correlation.
This should definitely help: http://financialexamhelp123.com/durbin-watson-statistic-test/
Here it is.
We have both positive and negetive serial correlation, value 2 denotes positive serial correlation, while values above 2 denote negative serial correlation.
Your question above is about positive serial correlation, thus because the DW value of 1.89 is above the upper band of the critical value, we fail to reject the null and conclude that there is no serial correlation problem.
We need the upper critical value to decide if the estimation falls in the inconclusive range, for instance, if the DW value was 1.65, if falls above the Dl, and below the Du, thus the analysis is inconclusive.
Hope that helps.
Thanks guys. I understand the concept well. I am just confirming if the critical values represented dl and du which you said it did.The exam does not mention “dl” and “dl” at all, so I was just making sure.
Lastly, DW test stat = 2(1-r). Will “r” always just be given to you? Or does it sit anywhere in a table? Every exam question I have seen just gives the DW test stat to you. “r” is never in the table. Does anyone know?
I assume r is always given (they won’t ask to compute the correlation coefficient of the residuals…imagine you have 500 residuals…!)
Awesome, that is what I was assuming but was not completely sure I understood what the number represented, but I did. Thanks!