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I want to fit an ARMA model with covariates to a non-stationary time series. I have daily measurements for water flow for 4 stations (S1-S4) and the time series is not stationary, so I will have to take a first difference.

I want to find an ARMA model that takes as covariates the other 3 stations.

What I have done:
a) m1 = auto.arima(S1, d=1, max.p, max.q, xreg=data.frame(S2,S3,S4))
b) m2 = auto.arima(diff(S1), d=0, max.p, max.q, xreg=data.frame(diff(S2),diff(S3),diff(S4)))

My question: which model is correct, considering the series are non-stationary?

I will appreciate any suggestion.

Thank you,
Patricia

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They are algebraically equivalent models, although the estimated coefficients will be slightly different due to the way the models are estimated.

Assuming you are actually interested in S1 rather than its differences, then you should use m1.

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