DW Question

Quick one for you quant folks, When using the DW test of 2(1-R) and looking up the values on the DW table, I am having a tough time interpreting the results. I’m looking at figure 6 on p 202 SS 3. I am not quite understanding the notation being used. Where did they get “4” from and what is 4-D1, 4-Du? Can someone explain?

the D-W test simply cuts up the region from 0-4 on the number chart into 5 parts -region 0 toDL is sign of pos serial correlation -region DL to DU is inconclusive -region DU to 4-DU is sign of no serial correlation -region 4-DU to 4-DL isinconclusive. -region 4-DL to 4 is neg serial correlation. Hope this helps

Don’t have the book in hand. 4 is the max value of 2*(1-r), since r is between -1 and 1.

So in the example on page 202, D1 is 1.34 and DU is 1.66 Stat falls Below 1.34 = Positive Serial Correlation Stat Falls Above 1.66 = Negative Serial Correlation Between 1.34 & 1.66 = Inconclusive What is he region for Do not reject? I am still missing something here

do u meean 2.66? as in 4-1.34=2.66? otherwise makes no sense to me

Correct me if I’m wrong, we are only expected to know: If DW < DL ====> positive S.C., If DW > DU ====> negative S.C., Between DL and DU it s inconclusive. Has anyone seen CFAI questions (Mock, sample, or book) which test the detailed chart?

to make it easy to memorize: positive AC: r is close to 1 ==> DW is close to 0, like 0-Dl negative AC: r is close to -1 ==> DW is close to 4, like 4-Dl no AC: r is close to 0 ==> DW is close to 2, like DU-(4-DU). Otherwise, inconclusive.

yeah, DW>Du does not necessarily imply negative serial correlation… This means that DW could be in the range of Du to 4-Du, in which case the null cannot be rejected (no serial corr.), OR DW could be in the range of 4-Du to 4-Dl, in which case the test is inconclusive, OR DW could be in the range of 4-Dl to 4, in which case there is negative serial correlation. I always just draw out the line: {--------------*------------------------*-------------------*------------*---------------} 0-------------Dl-----------------------Du-----------------4-Du--------4-Dl-----------4 And then remember the left side is positive serial corr, right side is negative, and middle section shows no serial corr.

Thanks Guys, Got it

So you want the DW to = 2 or as close to 2 as possible correct?

I would think you would want it to be greater than 2 because that would indicate Neg. serial correlation?

value of 2 means no serial correlation…

> Has anyone seen CFAI questions (Mock, sample, or book) which test the detailed chart? Anyone? There is no space in my head for trivial pursuit.

r>(1-Dl/2) ==> positive SC r negative SC r between (Du/2-1) and (1-Du/2) ==> no SC Du and DL are < 2. no quite useful for the exam.