# NDK_GARCH_LRVAR int __stdcall NDK_GARCH_LRVAR ( double mu, const double * Alphas, size_t p, const double * Betas, size_t q, WORD nInnovationType, double nu, double * retVal )

Calculates the long-run average volatility for the given GARCH model.

Returns
status code of the operation
Return values
 NDK_SUCCESS Operation successful NDK_FAILED Operation unsuccessful. See Macros for full list.
Parameters
 [in] mu is the GARCH model conditional mean (i.e. mu). [in] Alphas are the parameters of the ARCH(p) component model (starting with the lowest lag). [in] p is the number of elements in Alphas array [in] Betas are the parameters of the GARCH(q) component model (starting with the lowest lag). [in] q is the number of elements in Betas array [in] nInnovationType is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) INNOVATION_GAUSSIAN Gaussian Distribution (default) INNOVATION_TDIST Student's T-Distribution, INNOVATION_GED Generalized Error Distribution (GED) [in] nu is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function. [out] retVal is the calculated long run value
Remarks
1. The underlying model is described here.
2. The GARCH long-run average variance is defined as: $V_L=\frac{\alpha_o}{1-\sum_{i=1}^{max(p,q)}\left(\alpha_i+\beta_i\right)}$
3. The time series is homogeneous or equally spaced.
4. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
5. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
6. GARCH_CHECK examines the model's coefficients for:
• Coefficients are all positive
Requirements
 Namespace: NumXLAPI Class: SFSDK Scope: Public Lifetime: Static
 int NDK_GARCH_LRVAR ( double mu, double[] Alphas, UIntPtr p, double[] Betas, UIntPtr q, short nInnovationType, double nu, ref double retVal )

Calculates the long-run average volatility for the given GARCH model.

Return Value

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

 NDK_SUCCESS operation successful Error Error Code
Parameters
 [in] mu is the GARCH model conditional mean (i.e. mu). [in] Alphas are the parameters of the ARCH(p) component model (starting with the lowest lag). [in] p is the number of elements in Alphas array [in] Betas are the parameters of the GARCH(q) component model (starting with the lowest lag). [in] q is the number of elements in Betas array [in] nInnovationType is the probability distribution function of the innovations/residuals (see INNOVATION_TYPE) INNOVATION_GAUSSIAN Gaussian Distribution (default) INNOVATION_TDIST Student's T-Distribution, INNOVATION_GED Generalized Error Distribution (GED) [in] nu is the shape factor (or degrees of freedom) of the innovations/residuals probability distribution function. [out] retVal is the calculated long run value
Remarks
1. The underlying model is described here.
2. The GARCH long-run average variance is defined as: $V_L=\frac{\alpha_o}{1-\sum_{i=1}^{max(p,q)}\left(\alpha_i+\beta_i\right)}$
3. The time series is homogeneous or equally spaced.
4. The number of parameters in the input argument - alpha - determines the order of the ARCH component model.
5. The number of parameters in the input argument - beta - determines the order of the GARCH component model.
6. GARCH_CHECK examines the model's coefficients for:
• Coefficients are all positive
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