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I have a OLS model looks like this:

formula

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However, the residuals have auto-correlation like this:

enter image description here

It doesn't seem a strong autocorrelation, and the model passes the Engle-Granger cointegration test (package egcm). However, the model fails Durbin–Watson test. Adding an autoregressive term like AR(1) will totally solve this problem, because ARMAX explicitly models the errors. but I am a bit worried about the possibility of spurious regression.

Are my OLS model residuals good enough to conclude cointegration? If not, does ARMAX help in my case?

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