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Autocorrelation of Error: DW vs. t-test

Hi guys,

I’m a little hung up on when we need to use the DW test vs. a t-test. My understanding of serial correlation is that it is the correlation of our error term vs. itself at different lagging intervals: r( et , et-x ) 

We can solve for that value and then plug into the DW formula and see if there’s serial correlation. However when I review the section on Auto-Regressive models (testing a variable against itself) I saw that we CANNOT use DW to test for serial correlation in an AR model. 

I guess my confusion is that I understand Auto-Regression models to be regressing a variable against itself just like the correlation of error vs. error at a different point in time. So by that logic we can’t use a DW test on error. Do you see what I mean? Thanks

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DW can’t be used for AR time-series models because the independent variable is a lagged value of the dependent variable.