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

## Syntax

**ARMA_CHECK**(**Mean**, **sigma**, **phi**, **theta**)

**Mean**- is the ARMA model long-run 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.
- ARMA_CHECK checks the process for stability: stationarity, invertibility, and causality.
- Using the Solver add-in in Excel, you can specify the return value of ARMA_CHECK as a constraint to ensure a stationary ARMA model.
- The long-run mean can take any value or 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 may have missing values 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).

## Files Examples

## Related Links

## References

- D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906.
- 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.
- Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848.
- Walter Enders; Applied Econometric Time Series; Wiley; 4th edition(Nov 03, 2014), ISBN: 1118808568.

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