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

## Syntax

**SARIMAX_CHECK**(mean, **sigma**, **d**, **phi**, **theta**, **period**, **sd**, **sPhi**, **sTheta**, **Beta**)

**mean**- is the SARIMA model mean (i.e., long-run of the differenced time series). If missing, the mean is assumed zero.
**sigma**- is the standard deviation value of the model's residuals/innovations.
**d**- is the non-seasonal difference order.
**phi**- are the parameters of the non-seasonal AR model component AR(p) (starting with the lowest lag).
**theta**- are the parameters of the non-seasonal MA model component MA(q) (starting with the lowest lag).
**period**- is the number of observations per one period (e.g., 12 = Annual, 4 = Quarter).
**sd**- is the seasonal difference order.
**sPhi**- are the parameters of the seasonal AR model component AR(p) (starting with the lowest lag).
**sTheta**- are the parameters of the seasonal MA model component MA(q) (starting with the lowest lag).
**Beta**- are the coefficients array of the exogenous factors.

## Remarks

- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- SARIMA_CHECK checks if $\sigma\gt 0$ and if all the characteristic roots of the underlying ARMA model fall outside the unit circle.
- Using the Solver Add-in in Excel, you can specify the return value of SARIMA_CHECK as a constraint to ensure a stationary ARMA model.
- The intercept or the regression constant term input argument is optional. If omitted, a zero value is assumed.
- 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 SARIMA).
- The order of the parameters defines how the exogenous factor input arguments are passed.
- One or more parameters may have a missing value or an error code (i.e., #NUM!, #VALUE!, etc.).

- The long-run mean argument (mean) of the differenced regression residuals can take any value. If omitted, a zero value is assumed.
- The residuals/innovations standard deviation (sigma) must be greater than zero.
- For the input argument - phi (parameters of the non-seasonal AR component):
- The input argument is optional and can be omitted, in which case no non-seasonal AR component is included.
- The order of the parameters starts with the lowest lag.
- One or more parameters may have a missing value or an error code (i.e., #NUM!, #VALUE!, etc.).
- The order of the non-seasonal 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 (parameters of the non-seasonal MA component):
- The input argument is optional and can be omitted, in which case no non-seasonal 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 non-seasonal MA 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 - sPhi (parameters of the seasonal AR component):
- The input argument is optional and can be omitted, in which case no seasonal AR component is included.
- The order of the parameters starts with the lowest lag.
- One or more parameters may have a missing value or an error code (i.e., #NUM!, #VALUE!, etc.).
- The order of the seasonal 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 - sTheta (parameters of the seasonal MA component):
- The input argument is optional and can be omitted, in which case no seasonal 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 seasonal 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 non-seasonal integration order - d - is optional and can be omitted, in which case d is assumed zero.
- The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed zero.
- The season length - s - is optional and can be omitted, in which case s is assumed zero (i.e. Plain ARIMA).
- 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

- 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.

## Comments

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