# Durbin-Watson

What is the difference between DL and DU values on a DW table?

On the table you take the two values and they make up your line bare used to determine whether you accept or reject the hypothesis that auto correlation is present 0 ----- DLower — Dupper ---- 4 - DUpper ------ 4 - DLower -----4 If your calculated D stat is below Dlower, then Positive A/C is present Between DL and DU - inconclusive - you can’t reject and can’t not reject Greater than Dupper than positive A/C is not present And similar for negative A/c So its positive A/C - inconclusive - no A/C - inconclusive - negative A/C

thank you very much.

And its corrected with Hansen Std Errors

…and don’t use it with AR models. So how do you check for serial correlation in AR models?

keep adding lags until the residual slopes are no longer significant

U tesit for AR model, test for corrolation, still exists, test for AR2, if it doesnt exist, add a seasonality lag, then ARCH … Get st error = 1 / square root of number of observations t = AC / st error if its greater than t table, then it needs adjustment… if not then u fail to reject null and model is correctly specified.

That’s how you resolve them, but to spot them you check that all residuals are not significant, their t-stats not big. You can easily see it in the autocorrelation table.

thanks all, I was just quizzing to see who is interested.

true enough … Can you explain more on cointegration … I have no clue what that is … All i know is both v should not have unit root OR if they have unit root but must be cointegrated (long term economic relation) … And it has a reliable t test.

for AR use dickey fuller test. H0: b1-1 =0 if rejected, then time is covariant stationary. If fail to reject, then b1 is indeed 1/has unit root. To correct unit root, do first differencing. A) Calculate yt = error = xt - x(t-1) B) Then state yt = b0 + b1 y(t-1) + e where b0=b1=0

Cointegration – just like you do differencing to get rid of the rising or falling trend, cointegration says if the two series are bad (not cov station), then it’s ok, if the two series are relared to each other…they are both going wild, but if you take the difference between them, you get a stable mean, etc.

pepp Wrote: ------------------------------------------------------- > for AR use dickey fuller test. > H0: b1-1 =0 > if rejected, then time is covariant stationary. > If fail to reject, then b1 is indeed 1/has unit > root. > > > To correct unit root, do first differencing. > A) Calculate yt = error = xt - x(t-1) > B) Then state yt = b0 + b1 y(t-1) + e where > b0=b1=0 All the tests before whether hetero, serial, Autoregression … if we reject null = > model needs to be corrected however in this test, if we reject null then it is cov stationary and it doesnt have unit root? please confirm…

Just reviewed this section: For simple time series Trend Analyis, use dicky fuller and follow CFA_Chap’s analysis. For AR models, you need to perform a t-test on the autocorrelation or series correlation coefficients. If those are significant (generally greater than 2), then autocorrelation exists. This is also used for idenitfying seasonality I believe. For AR, there is also the ARCH test for conditional heteroskedasticity. Once again, if the t-stats on the coefficients are significant, the model is invalid and needs to be respecified. I do hope we don’t have to calculate, and can merely look at the reports 