# SARIMA_CHECK - Check parameters' values for model stability

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

## Syntax

SARIMA_CHECK(mean, sigma, d, phi, theta, period, sd, sPhi, sTheta)
mean
is the ARMA model mean (i.e. mu). If missing, mean is assumed to be 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 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).

## Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. SARIMA_CHECK checks if $\sigma\gt 0$ and if all the characteristic roots of the underlying ARMA model fall outside the unit circle.
4. 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.
5. The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
6. The residuals/innovations standard deviation (sigma) must be greater than zero.
7. 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 values or error codes (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).
8. 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).
9. 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 values or error codes (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).
10. 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).
11. The non-seasonal integration order - d - is optional and can be omitted, in which case d is assumed to be zero.
12. The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed to be zero.
13. The season length - s - is optional and can be omitted, in which case s is assumed to be zero (i.e. plain ARIMA).
14. The function was added in version 1.63 SHAMROCK.

## References

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