NDK_ARIMA_GOF

Computes the log-likelihood ((LLF), Akaike Information Criterion (AIC) or other goodness of fit function of the ARIMA 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 ARMA model mean (i.e. mu).
[in]	sigma	is the standard deviation of the model's residuals/innovations.
[in]	nIntegral	is the model's integration order.
[in]	phis	are the parameters of the AR(p) component model (starting with the lowest lag).
[in]	p	is the number of elements in phis (order of AR component)
[in]	thetas	are the parameters of the MA(q) component model (starting with the lowest lag).
[in]	q	is the number of elements in thetas (order of 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 GOF return 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 maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and providing estimates for the model's parameters.
7. The integration order argument (d) must be a positive integer.
8. The long-run mean can take any value or may be omitted, in which case a zero value is assumed.
9. The residuals/innovations standard deviation (sigma) must be greater than zero.
10. For the input argument (phi):
    • The input argument is optional and can be omitted, in which case no AR component is included.
    • The order of the parameters starts with the lowest lag.
    • One or more parameters can be missing or an error code (i.e. #NUM!, #VALUE!, etc.).
    • The order of the AR component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
11. For the input argument (theta):
    • The input argument is optional and can be omitted, in which case no 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 MA component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).

Exceptions

Exception Type	Condition
None	N/A

Requirements

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