# NDK_ARIMA_GOF

 int __stdcall NDK_ARIMA_GOF ( double * X, size_t nSize, double mean, double sigma, WORD nIntegral, double * phis, size_t p, double * thetas, size_t q, GOODNESS_OF_FIT_FUNC retType, double * retVal )

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

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
[in] X is the univariate time series data (a one dimensional array).
[in] nSize is the number of observations in X.
[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).
Requirements
Examples



 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 NDK_ARIMA_GOF ( double[] pData, UIntPtr nSize, double mean, double sigma, short nIntegral, double[] phis, UIntPtr p, double[] thetas, UIntPtr q, GOODNESS_OF_FIT_FUNC retType, ref double retVal )

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 SFSDK Public Static NumXLAPI.DLL
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