# DURBIN WATSON

Hello, Couple of q’s regarding durbin watson. -We approximate the DW stat by this 2(1-r) then there are 2 rules imo, i just wanna confirm. 1- in order to figure out whether it is positive or negative serial correlation, we use this test…if the dw stat (2*(1-r)) equals 2, inconclusive; if it is less than 2, then it is positive serial, and if its greater than 2, than its negative. 2- then we use the table, to figure out d1 and du, if its to the left of d1, we reject (or fail to reject, cant remember) and its is to the right du, we reject (or fail to reject, cant remember). If it is inbetween d1 and du, dit is inconclusive… Is this pretty much it? Is it really a 2 step process? Many thanks

you are right about the steps. 1) calculate statistic dw 2) identify dl, du. 3) if dw >= du - reject zero hypothesis -> negative serial correlation if dw <= dl - reject zero hypothesis -> positive serial correlation if dw is between dl and du, can’t reject zero hypothesis of no serial correlation

so either way u reject? i dunno… I remember something like this in the cfa… ______r_________d1________du________ftr_____________________________ where r= reject, and ftr is fail to reject. I do not have my notes with me, so the r and ftr could be reversed. but i specifically remeber them being different, and not a reject on both sides as you suggested. Thanks for the feedback though… any more idea’s…? or am i way off??

You are right, there is one more area in the middle that rejects positive serial correlation and negative serial correlation. http://en.wikipedia.org/wiki/Durbin–Watson_statistic

Im still confused… thanks anyhow… Ill come back with an example later on.

The DW is used to determine whether positive or negative autocorrelation exists. Step 1: Compute DW Stat 2: Identify the DL (Lower) and DU (Upper) 3: Interpret the result The step 3 is a bit complicated. I will try to explain it. +ve auto. exists--------Inconclusive-----No evidence-----Inconclusive----- -ve auto. exists |-------------------------|-------------------|---------------------|-------------------|--------------------| 0 DL DU ~2~ 4-DU 4-DL 4 IF DW Stat is below DL —> +ve autocorrelation exists If DW Stat is above 4-DL (4 minus DL) —> -ve autocorrelation exists If DW Stat is between DL and DU ----> the result is inconclusive IF DW Stat is between DU and 4-DU —> No evidence of autocorrelation IF DW Stat is between 4-DU and 4-DL ----> the result is inconclusive I forgot to mention, you have to get DL and DU value from the DW table. Sorry about the table. It seems that I couldnt leave any space without inserting any symbol. I hope this helps.

Ok, thanks, this make sence… But, how do you know if it ios positive or negative correlation? Is this where the 2(1-r) comes into play? I was under the assumption, if the calculated DW stat using the approximation above, is less than 2, then it is positive serial corr, and if it is more than 2, if is neg serial corr. If it is bang on 2, it is inconclusive… Then, i would dig up the d1 and du using the table, and use your line above to see if its rejected, or fail to reject… thanks for all the feedback guys…and gals?

ok, I re-read this at home, and get it now. One last question though, the 4-du or dl part is just math right? Does it stand for something other than number 4? thanks allot.

yes the thing on 4-dL and 4-dU is pure math… d approx. 2(1-r). If r is -1, i.e. perfect negative autocorelation, then d is approx. 4. Hope this helps in your understtanding.

You need the 4 because the DW test can result in a score of 0 to 4. Therefore, to draw the line from reject - inconclusive - accept - inconclusive - reject as gan drew it, you need to set the boundaries. The boundary from reject to inconclusive is the DL. So 0 to DL 0 -> reject the null. Then from DL to DU you cannot reject or accept the null. Within DU and 4-DU you accept the null, 4-DU to 4-DL you cannot do both again and from 4-DL to 4 you reject it. Say DL is 0,8 and DU is 1,2. (bad example in real life but just to make the point) Then: 0 to 0,8 -> reject 0,8 to 1,2 -> inconclusive 1,2 to (4 - 1,2 = 2,8) -> accept 2,8 to 3,2 -> inconclusive 3,2 to 4 -> reject the null. 4 comes from 2(1-r) and since r can be -1 to +1 your outcome can vary from 2(1-1) = 0 to 2(1–1) = 4 Hope this helps.

Should we know how to calculate dl and du from the tables? If so which table do we use? Thanks.

dl and du are in the tables, under critical values of the durbin watson statistic, surprisingly enough. Yes, you need to know how to use the table, and how many degrees of freedom to look for.

Simple enough. Thanks chrismaths.

2009 los 12g: discuss types of heteroskadastity and the effects of heteroskedastity and serial correlation on statistical inference. It says basically to know about durban Watson above I think - def doesn’t say calculate - but why all of these formulas in the book? It doesn’t even say ‘interpret’ - so all of the above seems excessive, or am I reading this los wrong, or has it changed since last year?

I don’t think you’d need to calculate the DW stat. I am expecting it to be given.

You will not have to “calculate” it, nor will you be given a separate DW table. If you see a question on the exam, the DW stat will be given, and it will be obviously significant. The main points you need to know is that the presence of autocorrelation will not affect the biasedness or consistency of the estimators, but it will render them inefficient. The std. errors will be downwardly biased, R^2 will likely be overstated, and significance tests will be misleading. If using for predictive purposes only, the problem is not very dire, but if using the model for inferences, spurious results can easily occur.