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, 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 (i.e. MA(q)) (starting with the lowest lag).

**period** is the 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 (i.e. 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 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 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 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 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

## 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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