Returns an array of cells for the quick guess, optimal (calibrated), or std. errors of the values of the model's parameters.

## Syntax

**SARIMA_PARAM**(**X**, Order, mean, **sigma**, **d**, **phi**, **theta**, **period**, **sd**, **sPhi**, **sTheta**, Type, MaxIter)

**X**- is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).
**Order**- is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).
Order Description 1 ascending (the first data point corresponds to the earliest date) ( **default**).0 descending (the first data point corresponds to the latest date). **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 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).
**Type**- is an integer switch to select the output array: (1 = Quick Guess (default), 2 = Calibrated, 3 = Std. Errors).
Order Description 1 Quick guess (non-optimal) of parameters' values ( **default**).2 Calibrated (optimal) values for the model's parameters. 3 Standard error of the parameters' values. **MaxIter**- is the maximum number of iterations used to calibrate the model. If missing, the default maximum of 100 is assumed.

## Remarks

- The underlying model is described here.
- The time series is homogeneous or equally spaced.
- The time series may include missing values (e.g., #N/A) at either end.
- SARIMA_PARAM returns an array for the values (or errors) of the model's parameters in the following order:
- $\mu$.
- $\phi_1,\phi_2,...,\phi_p$.
- $\theta_1,\theta_2,...,\theta_q$.
- $\Phi_1,\Phi_2,...,\Phi_P$.
- $\Theta_1,\Theta_2,...,\Theta_Q$.
- $\sigma$.

- The long-run mean argument (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 (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).

- 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 values or error codes (i.e., #NUM!, #VALUE!, etc.).
- The order of the seasonal AR component model is solely determined by 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 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 to be zero.
- The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed to be zero.
- The season length - s - is optional and can be omitted, in which case s is assumed to be zero (i.e., plain ARIMA).
- The function was added in version 1.63 SHAMROCK.

## Files Examples

## Related Links

## 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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