NDK_SARIMA_GOF

Computes the log-likelihood ((LLF), Akaike Information Criterion (AIC) or other goodness of fit function of the SARIMA model.

Return Value

a value from NDK_RETCODE enumeration for the status of the call. 

NDK_SUCCESS	operation successful
Error	Error Code

Parameters

[in]	pData	is the univariate time series data (a one dimensional array).
[in]	nSize	is the number of observations in pData.
[in]	mean	is the model mean (i.e. mu).
[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]	retType	is a switch to select a fitness measure: Order   Description 1 Log-Likelihood Function (LLF) (default) 2 Akaike Information Criterion (AIC) 3 Schwarz/Bayesian Information Criterion (SIC/BIC) 4 Hannan-Quinn information criterion (HQC)
[out]	retVal	is the calculated goodness of fit 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. The residuals/innovations standard deviation (i.e. \(\sigma\)) should be greater than zero.
5. The ARMA model has independent and normally distributed residuals with constant variance. The ARMA log-likelihood function becomes: \[ \ln L^* = -T\left(\ln 2\pi \hat \sigma^2+1\right)/2 \] Where:
   • \(\hat \sigma\) is the standard deviation of the residuals.
6. The value of the input argument - period - must be greater than one, or the function returns #VALUE!.
7. The value of the seasonal difference argument - sD - must be greater than one, or the function returns #VALUE!.
8. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.
9. The long-run mean argument (mean) can take any value or be omitted, in which case a zero value is assumed.
10. The residuals/innovations standard deviation (sigma) must be greater than zero.
11. 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).
12. 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).
13. 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).
14. 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).
15. The non-seasonal integration order - d - is optional and can be omitted, in which case d is assumed to be zero.
16. The seasonal integration order - sD - is optional and can be omitted, in which case sD is assumed to be zero.
17. The season length - s - is optional and can be omitted, in which case s is assumed to be zero (i.e. plain ARIMA).

Exceptions

Exception Type	Condition
None	N/A

Requirements

Namespace	NumXLAPI
Class	SFSDK
Scope	Public
Lifetime	Static
Package	NumXLAPI.DLL

Examples