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

## Syntax

**ARIMA_CHECK** (µ, **σ**, [φ], [θ])

**µ**- Optional. Is the ARMA model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.
**σ**- Required. Is the standard deviation value of the model's residuals/innovations.
**[φ]**- Optional. Are the parameters of the AR(p) component model: [φ1, φ2 … φp] (starting with the lowest lag).
**[θ]**- Optional. Are the parameters of the MA(q) component model: [θ1, θ2 … θq] (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 long-run mean can take any value or may be omitted, in which case a zero value is assumed.
- The residuals/innovations standard deviation (σ) must be greater than zero.
- For the input argument ([φ]):
- 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 ([θ]):
- 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

## Related Links

- Wikipedia - Likelihood function.
- Wikipedia - Likelihood principle.
- Wikipedia - Autoregressive moving average model.

## References

- James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
- Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.

## Comments

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