I have some basic Arima questions.I built the following two Arima models in R (output below) and the R output each time mentions something about the mean being non-zero or zero.

Model 1:
ARIMA(1,0,0)(1,0,0)[12] with zero mean 

         ar1    sar1
      0.7232  0.3644
s.e.  0.0999  0.1434
Model 2:
ARIMA(1,0,0)(1,0,0)[12] with non-zero mean 

         ar1    sar1     mean
      0.9645  0.3081  70.8936
s.e.  0.0252  0.1288  18.6623

In Model 1, what does it mean for the Arima model to have zero mean - does it mean the response series has zero mean or that the residuals have zero mean? What would be the corresponding model equation? Similarly, Model 2 is Arima(1,0,0)(1,0,0)[12] with non-zero mean - again is this saying something about the level of the response series or the residuals?

Also, I am confused about the intuitive meaning of a seasonal order - what does it mean to have an SAR1 term in the model in terms of the response series? Would much appreciate any replies that can help me understand the intuition or at least the model equation.

  • 1
    $\begingroup$ What does it mean for the Arima model to have zero mean?- It means that an intercept term is excluded from your ARIMA model (Mean is an intercept term). $\endgroup$ – Dato Gogolashvili Jan 25 at 10:28
  • $\begingroup$ Could you make your title more specific? $\endgroup$ – Richard Hardy Jan 25 at 16:29

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