mean is the ARMA model long-run mean (i.e. mu). If missing, mean is assumed to be zero.

sigma is the standard deviation of the model's raw residuals (aka innovations or shocks).

phi are the parameters of the auto-regressive (i.e AR) component model (starting with the lowest lag).

theta are the parameters of the moving-average (i.e. MA) component model (starting with the lowest lag).

1. The underlying model is described here.
2. The long-run mean can take any value or can be omitted, in which case a zero value is assumed.
3. The residuals/innovations standard deviation (sigma) must be greater than zero.
4. For the input argument (phi):
   • The input argument is optional and can be omitted, in which case no AR component is included.
   • The order of the parameters starts with the lowest lag.
   • One or more parameters may have missing values or error codes (i.e. #NUM!, #VALUE!, etc.).
   • The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
5. For the input argument (theta):
   • The input argument is optional and can be omitted, in which case no MA component is included.
   • The order of the parameters starts with the lowest lag.
   • One or more values in the input argument can be missing or an error code (i.e. #NUM!, #VALUE!, etc.).
   • The order of the MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).