Examines the model's parameters for stability constraints (e.g. stationarity, invertibility, causality, etc.)

## Syntax

**ARIMA_CHECK**(

**mean**,

**sigma**,

**phi**,

**theta**)

**mean** is the ARMA model mean (i.e. mu).

**sigma** is the standard deviation of the model's residuals/innovations.

**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

- The underlying model is described here.
- ARIMA_CHECK checks the ARMA model for stability: stationarity, invertibility, and causality.
- The integration order argument (d) must be a positive integer.
- The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
- The residuals/innovations standard deviation (sigma) must be greater than zero.
- 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).

- 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).

- The function was added in version 1.63 SHAMROCK.

## Files Examples

## 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

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