# SARIMA - SARIMA Model Definition

Returns a unique string identifier to designate the specified SARIMA model.

## Syntax

SARIMA(mean, sigma, d, phi, theta, period, sd, sPhi, sTheta)

mean is the ARMA model mean (i.e. mu). If missing, the mean is assumed to be zero.

sigma is the standard deviation value of the model's residuals/innovations.

d is the non-seasonal integration 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 period (e.g. 12=Annual, 4=Quarter).

sd is the seasonal integration 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 long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
3. The residuals/innovations standard deviation (sigma) must be greater than zero.
4. 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).
5. 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).
6. 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).
7. 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).
8. The non-seasonal integration order - d - is optional and can be omitted, in which case d is assumed to be zero.
9. The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed to be zero.
10. The season length - s - is optional and can be omitted, in which case s is assumed to be zero (i.e. plain ARIMA).
11. The function was added in version 1.63 SHAMROCK.

## References

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