ARIMA - Defining an ARIMA Model

Returns a unique string to designate the specified ARIMA model.

Syntax

ARIMA(D, mean, sigma, phi, theta)

D

is the integration order.

mean

is the ARMA model 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 integration order argument (d) must be a positive integer.
3. The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
4. The residuals/innovations standard deviation (sigma) must be greater than zero.
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 can be missing or an error code (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).
7. The function was added in version 1.63 SHAMROCK.

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.