# NDK_SARIMAX_PARAM

 int __stdcall NDK_SARIMAX_PARAM ( double * pData, double ** pFactors, size_t nSize, size_t nFactors, double * fBetas, double * mean, double * sigma, WORD nIntegral, double * phis, size_t p, double * thetas, size_t q, WORD nSIntegral, WORD nSPeriod, double * sPhis, size_t sP, double * sThetas, size_t sQ, MODEL_RETVAL_FUNC retType, size_t maxIter )

Returns an array of cells for the initial (non-optimal), optimal or standard errors of the model's parameters.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
[in,out] pData is the univariate time series data (a one dimensional array).
[in] pFactors  is the exogneous factors time series data (each column is a separate factor, and each row is an observation).
[in] nSize is the number of observations.
[in] nFactors  is the number of exognous factors
[in,out] mean is the mean of the differenced time series process
[in,out] sigma is the standard deviation of the model's residuals/innovations.
[in] nIntegral is the non-seasonal difference order
[in,out] phis are the coefficients's values of the non-seasonal AR component
[in] p is the order of the non-seasonal AR component
[in,out] thetas are the coefficients's values of the non-seasonal MA component
[in] q is the order of the non-seasonal MA component
[in] nSIntegral  is the seasonal difference
[in] nSPeriod  is the number of observations per one period (e.g. 12=Annual, 4=Quarter)
[in,out] sPhis are the coefficients's values of the seasonal AR component
[in] sP is the order of the seasonal AR component
[in,out] sThetas are the coefficients's values of the seasonal MA component
[in] sQ is the order of the seasonal MA component
[in] retType is a switch to select the type of value returned: 1= Quick Guess, 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
[in] maxIter is the maximum number of iterations used to calibrate the model. If missing or less than 100, the default maximum of 100 is assumed.
Remarks
1. The underlying model is described here.
2. The time series is homogeneous or equally spaced
3. The time series may include missing values (e.g. NaN) at either end.
4. Each column in the explanatory factors input matrix (i.e. X) corresponds to a separate variable.
5. Each row in the explanatory factors input matrix (i.e. X) corresponds to an observation.
6. Observations (i.e. rows) with missing values in X or Y are assumed missing.
7. The number of rows of the explanatory variable (X) must be at equal to the number of rows of the response variable (Y).
8. The intercept or the regression constant term input argument is optional. If omitted, a zero value is assumed.
9. 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.).
10. The long-run mean argument (mean) of the differenced regression residuals can take any value. If omitted, a zero value is assumed.
11. The residuals/innovations standard deviation (sigma) must greater than zero.
12. 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
• 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).
13. 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
• 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).
14. 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
• 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).
15. 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
• 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).
16. The non-seasonal integration order - d - is optional and can be omitted, in which case d is assumed zero.
17. The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed zero.
18. The season length - s - is optional and can be omitted, in which case s is assumed zero (i.e. Plain ARIMA).
Requirements