S2000 Magician. If you can help with this — I will love it. Or anybody else but I got a feeling S2000 might be the goto guy here.
How does the Unit root test not conflict with the test for Serial Correlation for AR models. test On Page 430 it states “For a stationary time series either AUTOCORRELATIONS at ALL lags are indistinguishable from 0 OR it rapidly drops off to zero as lags become large”
For the second part focusing on as the LAGS beome large it drops off to 0. That would mean the autocorrelations are not 0 (Say for example for the first 3 and then drops right to 0). In this case we would Reject that the autocorrelcation = 0 at the first 3 lags and then Fail to reject afterwards). Then we could say there is No Unit root and it’s covariance stationary and the AR Model fits by that logic.
But with that same idea — Using the Test for serial correlation using the autocorrelations — Using the same numbers we would Reject the null hypothesis the autocorrelations = 0 -----> Therefor they are serial correlated and the AR model can NOT be used. The two ideas conflict.
Another Conflict. Comparing MA models with AR models using the autocorrelations. There’s an example given on page 437 where the autocorrelations are ALL near 0 and you fail to to reject and conclude it comes from an MA(0) model. It states later the for an AR(1) model the first autocorrelation would differ significantly from 0 and the autocorrelations would have gradually declined. 1. If the first autocorrelation is signficantly different then 0 then it would be serially correlated and it couldn’t come from an AR 1 model. 2. There’s two examples in the text (Eg. 9 and 10). All the autocorrelations are near 0 and you fail to reject —> it then concludes they’re not serially correlated and the AR model fits. At the first lag it is NOT signficantly different then 0 as example 14 states at the end on page 438.
So that’s my confusion.