ARMAX - Defining an ARMA model

Returns a unique string to designate the specified ARMAX model.

Syntax

ARMAX(Beta, mean, sigma, phi, theta)

Beta

is the coefficients array of the exogenous factors.

mean

is the ARMA long-run mean (i.e., mu).

sigma

is the standard deviation of the model's residuals.

phi

are the parameters of the AR(p) component model (starting with the lowest lag).

theta

are the parameters of the MA(q) component model (starting with the lowest lag).

Remarks

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.