Could someone confirm this? For trend models, serial correlation is tested using DW: if |DW| > critiical DW, there is NO positive serial correlation. For AR models, serial correlation is tested using t-scores: If the t-statistics of ALL the autocorrelations of the lagged residulas are > than the t-critical, then THERE IS serial correlation. I guess I’m trying to confirm the null hypothesis is different in the two tests: in the Trend model it is set as ThERE IS serial correlation, and in the AR model, it is set as THERE IS NO serial correlation.
i don’t think that’s it. i think DW gives you a lower and an upper range- if you’re lower than the low critical, you have positive serial correlation. if you’re in between the range, i think inconclusive. if you’re above the range, negative seriall correlation. (from what i remember, haven’t looked at quant in ages). you can’t use a DW for AR models. # near 2 is normally no serial correlation… as you get closer to 0 and 4, houston, you may have a problem.
Durbin watson has 5 areas 0…dl…du…4-du…4-dl…4 …positive…indeterminate…do not reject…indeterminate…negative…
right- thx for the picture. i forgot the do not reject zone.
How are we supposed to apply this on the exam?? Are we provided with the upper and lower bounds, and basically plug and chug into CPK’s diagram above?
Both of you are correct: if |DW| < critiical DW, there is positive correlation. But in the AR model, it’s kind of the opposite because the null hypothesis is stated differently: If t-statistics of ALL autocorrelations < t-critical, there is NO serial correlation.
AR Model - yes it is like that. If all the T-stats are less than T-Crit - there is no autocorrelation. and the t-stat calc = 1/sqrt(n) where n=# of time periods.
i don’t think it says anywhere CALCULATE with regards to DW, but both the texts and schweser do some calcs on it. i would almost guess that if these all fall into quant, it’d be more check out your anova whatever table, tell me what this might suffer from, and maybe a 2 parter how do you fix it? i’m thinking they prob wouldn’t ask a calc but just in case, they’re not that bad to do. i will wait for cpk to remind me of the formula- it’s like blah(1 - blah) gets you to your # and then you just look that up in the durbin watson table. that’s right… i don’t remember the formula at all right now and i’ll just patiently wait for cpk to post it up. i guess C.
> t-stat calc = 1/sqrt(n) where n=# of time periods I don’t think this is for t-stat. The t-stat you just read it off of the table or do this: t-stat = Autocorrelation Value of lagged residual / std error, both are in the table.
sorry this is the std error - I got confused and put it as t-stat.
> t-stat calc = 1/sqrt(n) where n=# of time periods actually that’s for finding std error of lagged residual, but like banni said, these should all be given to you, you just need to interpret them.
in case they do not, and still ask you to make a calculation - for a time series with autocorrelation - std error of the lagged residual = 1/sqrt(n).
which means ALL lagged residuals have same std error.
they do, if you see the charts anywhere.
Summing it up: 1) Testing for Autocorrelation in Trend Model: - Use Durbin Watson test-statistic (usually given) If t-stat < below lower limit = Positive Autocorrelation If t-stat > higher limit = Negative Autocorrelation 2) Testing for Error Terms Autocorrelation in ARCH Model: - Use t-stat calculated as follows: Autocorrelation Coefficient/Std. Error where Std. Error = 1/sqrt(n) n = Sample Size If Coefficient significantly different from 0, then there is no error terms serial correlation in the data set. Autocorrelation is used interchangeably with Serial Correlation
And if there is serial correlation in an AR(1) model, what do you do next?
If there is serial correlation, lags corresponding to the significant correlation are included in the model and tested again for error terms serial correlation.
look for the coefficient that has the “t-stat” out of whack. The first such one becomes a lagged variable. now redo the regression - and check again - to see if any of the t-stats for the autocorrelation coefficients is out of whack again. and so on… if you have run out of autocorrelation coefficients - move to a AR(2) model. and continue ad-nauseum, ad-infinitum.
Use AR(2) and see if there is still autcorrelation.
bannisja Wrote: ------------------------------------------------------- > i don’t think it says anywhere CALCULATE with > regards to DW thats what I was thinking