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an equation has to be covariance stationary for it to be economically significant.

DW test can be used in a trend model, but not in an AR(X) model. AR(X) model by definition is a model where data in one period depends on data in prior periods, and by that definition would definitely have serial correlation.

in the last case - you would first add the last significant T-stat - in this case 4.
then check the new model autocorrelations again.
at that point all of the autocorrelations should have become insignificant.

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