ARMAX - Defining an ARMA model

1. The underlying model is described here.
2. The long-run mean can take any value or 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 (beta):
   • The input argument is optional and can be omitted, in which case no regression component is included (i.e. plain ARMA).
   • The order of the parameters defines how the exogenous factor input arguments are passed.
   • One or more parameters may have missing values or error codes (i.e. #NUM!, #VALUE!, etc.).
5. 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).
6. 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).

Files Examples

Related Links

• Wikipedia - Autoregressive moving average model

References

• Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740