I have a OLS model looks like this:
However, the residuals have auto-correlation like this:
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?
