# NDK_SARIMAX_FORE

 int __stdcall NDK_SARIMAX_FORE ( 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, size_t nStep, FORECAST_RETVAL_FUNC retType, double alpha, double * retVal )

Calculates the out-of-sample forecast statistics.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
[in] 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] fBetas is the weights or loading of the exogneous factors
[in,out] mean is the mean of the ARMA process
[in] sigma is the standard deviation of the model's residuals/innovations.
[in] nIntegral is the non-seasonal difference order
[in] phis are the coefficients's values of the non-seasonal AR component
[in] p is the order of the non-seasonal AR component
[in] 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] sPhis are the coefficients's values of the seasonal AR component
[in] sP is the order of the seasonal AR component
[in] sThetas are the coefficients's values of the seasonal MA component
[in] sQ is the order of the seasonal MA component
[in] nStep is the forecast time/horizon (expressed in terms of steps beyond end of the time series).
[in] retType is a switch to select the type of value returned:
Order  Description
1  Fitted mean (default)
2  Fitted standard deviation or volatility
3  Raw (non-standardized) residuals
4  Standardized residuals
[in] alpha is the statistical significance level. If missing, a default of 5% is assumed.
[out] retVal is the calculated forecast value
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 time series may include missing values (e.g. NaN) at either end.
9. The intercept or the regression constant term input argument is optional. If omitted, a zero value is assumed.
10. For the input argument - Beta:
• The input argument is optional and can be ommitted, in which case no regression component is included (i.e. plain SARIMA).
• The order of the parameters defines how the exogneous factor input arguments are passed.
11. The long-run mean argumen (mean) of the differenced regression residuals can take any value. If ommitted, a zero value is assumed.
12. The residuals/innovations standard deviation (sigma) must greater than zero.
13. For the input argument - phi (parameters of the non-seasonal AR component):
• The input argument is optional and can be ommitted, 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).
14. For the input argument - theta (parameters of the non-seasonal MA component):
• The input argument is optional and can be ommitted, 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).
15. For the input argument - sPhi (parameters of the seasonal AR component):
• The input argument is optional and can be ommitted, 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).
16. For the input argument - sTheta (parameters of the seasonal MA component):
• The input argument is optional and can be ommitted, 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).
17. The non-seasonal integration order - d - is optional and can be ommitted, in which case d is assumed zero.
18. The seasonal integration order - sD - is optional and can be ommitted, in which case sD is assumed zero.
19. The season length - s - is optional and can be ommitted, in which case s is assumed zero (i.e. Plain ARIMA).
Requirements
Header SFSDK.H SFSDK.LIB SFSDK.DLL
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
* D. S.G. Pollock; Handbook of Time Series Analysis, Signal Processing, and Dynamics; Academic Press; Har/Cdr edition(Nov 17, 1999), ISBN: 125609906
* Box, Jenkins and Reisel; Time Series Analysis: Forecasting and Control; John Wiley & SONS.; 4th edition(Jun 30, 2008), ISBN: 470272848