# NDK_AIRLINE_GOF

 int __stdcall NDK_AIRLINE_GOF ( double * pData, size_t nSize, double mean, double sigma, WORD S, double theta, double theta2, GOODNESS_OF_FIT_FUNC retType, double * retVal )

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

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] nSize is the number of observations in pData.
[in] mean is the model mean (i.e. $$\mu$$).
[in] sigma is the standard deviation ( $$\sigma$$) of the model's residuals/innovations.
[in] S is the length of seasonality (expressed in terms of lags, where s > 1).
[in] theta is the coefficient of first-lagged innovation ( $$\theta$$)(see model description).
[in] theta2 is the coefficient of s-lagged innovation ( $$\Theta$$) (see model description).
[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 value of the goodness of fit.
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 airline model with order $$s$$ has 4 parameters: $$\mu\,,\sigma\,\,,\theta\,,\Theta$$
5. The Airline model is a special case of multiplicative seasonal ARIMA model, and it assumes independent and normally distributed residuals with constant variance.
Requirements
Examples



 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_AIRLINE_GOF ( double[] pData, UIntPtr nSize, double mean, double sigma, short dSeason, double theta, double theta2, 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 AirLine model.

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] nSize is the number of observations in pData.
[in] mean is the model mean (i.e. $$\mu$$).
[in] sigma is the standard deviation ( $$\sigma$$) of the model's residuals/innovations.
[in] dSeason is the length of seasonality (expressed in terms of lags, where s > 1).
[in] theta is the coefficient of first-lagged innovation ( $$\theta$$)(see model description).
[in] theta2 is the coefficient of s-lagged innovation ( $$\Theta$$) (see model description).
[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 value of the goodness of fit.
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 airline model with order $$s$$ has 4 parameters: $$\mu\,,\sigma\,\,,\theta\,,\Theta$$
5. The Airline model is a special case of multiplicative seasonal ARIMA model, and it assumes independent and normally distributed residuals with constant variance.
Exceptions
Exception Type Condition
None N/A
Requirements
Namespace NumXLAPI SFSDK Public Static NumXLAPI.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